Daily Papers

Weak-to-strong generalization asks whether stronger models can learn from weaker supervisors and surpass them. This question is particularly important for successive model generations and multi-domain consolidation, where repeating frontier-scale post-training from scratch can be prohibitively expensive. Yet conventional distillation treats the weak teacher as an optimization target, potentially imposing its capacity ceiling on the student. We introduce On-Policy Reverse Distillation (OPRD), which evaluates the teacher's policy shift relative to its reference policy on student rollouts and amplifies the component of the student's verifier-driven policy gradient along that direction. By rescaling only verifier-supported updates, OPRD preserves the stationary points of policy optimization while accelerating learning beyond the teacher. In both successive model transfer and multi-teacher distillation, OPRD achieves higher performance with fewer student updates than existing RL and distillation approaches. Response-style analysis shows that OPRD students remain closer to models trained with verifier-based RL alone than to their weak teachers, suggesting that teacher guidance accelerates rather than redirects the student's own optimization. Results in conventional strong-to-weak distillation further demonstrate that OPRD effectively combines verifier-driven policy optimization with teacher guidance regardless of capacity ordering.

Large reasoning models often solve problems through long chain-of-thought (CoT) traces, yet much of this computation is spent on redundant derivations, repeated self-verification, and detours that do not improve the final answer. Existing on-policy self-distillation methods reduce this cost by matching a student model to a concise copy of itself on prefixes sampled from the student's own rollouts. We show that this objective has an initialization bottleneck. Since supervision is applied only to visited prefixes, training from a verbose base model places the KL loss on contexts that are often noisy, redundant, or already off track. In such regions, a concise teacher can provide only local corrections, while the student continues to explore trajectories that an efficient reasoner should avoid. In this paper, we propose BIRD(Bootstrapped Iterative Self-Reasoning Distillation), a two-stage self-reasoning distillation method that improves the rollout distribution before on-policy training. BIRD first samples concise solutions from the base model under a brevity instruction, keeps only answer-correct traces, and performs a lightweight prompt-switch SFT step. The traces are generated with the brevity instruction but learned under the original task prompt, turning instruction-induced conciseness into a default reasoning behavior. Starting from this warm model, BIRD then applies on-policy reverse-KL distillation with a concise self-teacher, now on cleaner and more informative prefixes. Across Qwen3 series models, BIRD achieves a stronger accuracy-efficiency trade-off than prompting and cold-start on-policy distillation on MATH-500 and AIME benchmarks. On Qwen3-8B, it improves MATH-500 accuracy from 86.2% to 92.0% while reducing the average response length from 3,099 to 1,115 tokens. These results highlight prefix support as a central factor in efficient reasoning distillation.

On-policy distillation (OPD) has become a core technique in the post-training of large language models, yet its training dynamics remain poorly understood. This paper provides a systematic investigation of OPD dynamics and mechanisms. We first identify that two conditions govern whether OPD succeeds or fails: (i) the student and teacher should share compatible thinking patterns; and (ii) even with consistent thinking patterns and higher scores, the teacher must offer genuinely new capabilities beyond what the student has seen during training. We validate these findings through weak-to-strong reverse distillation, showing that same-family 1.5B and 7B teachers are distributionally indistinguishable from the student's perspective. Probing into the token-level mechanism, we show that successful OPD is characterized by progressive alignment on high-probability tokens at student-visited states, a small shared token set that concentrates most of the probability mass (97%-99%). We further propose two practical strategies to recover failing OPD: off-policy cold start and teacher-aligned prompt selection. Finally, we show that OPD's apparent free lunch of dense token-level reward comes at a cost, raising the question of whether OPD can scale to long-horizon distillation.

Large Audio Language Models (LALMs) have garnered significant research interest. Despite being built upon text-based large language models (LLMs), LALMs frequently exhibit a degradation in knowledge and reasoning capabilities. We hypothesize that this limitation stems from the failure of current training paradigms to effectively bridge the acoustic-semantic gap within the feature representation space. To address this challenge, we propose CORD, a unified alignment framework that performs online cross-modal self-distillation. Specifically, it aligns audio-conditioned reasoning with its text-conditioned counterpart within a unified model. Leveraging the text modality as an internal teacher, CORD performs multi-granularity alignment throughout the audio rollout process. At the token level, it employs on-policy reverse KL divergence with importance-aware weighting to prioritize early and semantically critical tokens. At the sequence level, CORD introduces a judge-based global reward to optimize complete reasoning trajectories via Group Relative Policy Optimization (GRPO). Empirical results across multiple benchmarks demonstrate that CORD consistently enhances audio-conditioned reasoning and substantially bridges the audio-text performance gap with only 80k synthetic training samples, validating the efficacy and data efficiency of our on-policy, multi-level cross-modal alignment approach.

Audio-language models (ALMs) can exploit textual shortcuts to answer questions while overlooking acoustic evidence, weakening audio understanding. On-policy distillation (OPD) trains compact ALMs by supervising student-generated responses with teacher predictions, but does not explicitly distinguish acoustic support from linguistic predictability. We propose Reward-Tilted On-Policy Distillation (RT-OPD) to strengthen acoustic grounding. Given the same question and student-generated text, a frozen teacher predicts the next token with and without audio inputs. Their log-probability contrast defines a reward that reshapes the teacher distribution for reverse-KL distillation, emphasizing the additional evidence provided by audio. Across two compact students and three benchmarks, RT-OPD consistently outperforms Vanilla OPD. Experiments with silenced and replacement audio further suggest that RT-OPD strengthens the student's reliance on acoustic evidence. Our 3B model achieves 72.72% accuracy on MMAU, the highest among the compared 3B models and competitive with several 7B and 8B models. Code and model checkpoints are available at https://github.com/KaiyangLi1992/RT-OPD.

On-policy distillation transfers reasoning capabilities by training a student model on its own generated trajectories using token-level feedback from a teacher. However, we identify a critical bottleneck, Supervision Fidelity Decay (SFD): as student-generated prefixes lengthen, the teacher's next-token distribution becomes less confident and less discriminative. Consequently, the teacher-dependent corrective signal in reverse-KL distillation weakens, causing student drift to compound across long reasoning chains. To mitigate SFD, we introduce Lookahead Group Reward (\ours{)}. Building on the insight that next-step teacher confidence reflects the discriminative strength of future reverse-KL supervision, evaluates the student's top-K candidate tokens by the teacher confidence they induce at the subsequent step and assigns a group-normalized reward. To maintain computational efficiency, we further design an entropy-triggered tree-attention mechanism. Across six math and code benchmarks, improves mean@8 by 2.57 points over OPD for a 7B student, with gains increasing in longer-generation and reaching +4.92 points on AIME-26 at 39k tokens.

Although pre-trained Vision-Language-Action (VLA) models exhibit impressive generalization in robotic manipulation, post-training remains crucial to ensure reliable performance during deployment. However, standard offline Supervised Fine-Tuning (SFT) suffers from distribution shifts and catastrophic forgetting of pre-trained capabilities, while online Reinforcement Learning (RL) struggles with sparse rewards and poor sample efficiency. In this paper, we propose On-Policy VLA Distillation (VLA-OPD), a framework bridging the efficiency of SFT with the robustness of RL. Instead of relying on sparse environmental rewards, VLA-OPD leverages an expert teacher to provide dense, token-level supervision on the student's self-generated trajectories. This enables active error correction on policy-induced states while preserving pre-trained general capabilities through gentle alignment. Crucially, we formulate VLA-OPD via a Reverse-KL objective. Unlike standard Forward-KL that induces mode-covering entropy explosion, or Hard-CE that causes premature entropy collapse, our bounded mode-seeking objective ensures stable policy learning by filtering out the teacher's epistemic uncertainty while maintaining action diversity. Experiments on LIBERO and RoboTwin2.0 benchmarks demonstrate that VLA-OPD significantly improves sample efficiency over RL and robustness over SFT, while effectively mitigating catastrophic forgetting during post-training.

On-policy distillation (OPD) supervises a student on its own trajectories with token-level signals from a frozen teacher, yet how a sampled loss allocates updates across tokens remains poorly understood. We analyze the gradient of the per-token K2 estimator of reverse KL with respect to the student logits. The ell_1 norm of this gradient factorizes into the absolute teacher--student log-probability gap and a student-side softmax factor that grows as the sampled token becomes less likely under the student. In our math-distillation runs, these per-token norms are highly non-uniform: low-student-probability tokens account for a disproportionate share of their sum and are also enriched in large teacher--student gaps. As a lightweight intervention suggested by this analysis, we study Surprise-aware Reweighting (SuRe), a detached, bounded weighting rule that further amplifies this existing allocation. Across two Qwen3 student scales, SuRe improves several math metrics over vanilla OPD and shows no clear degradation on the selected out-of-domain benchmarks. Our primary contribution is therefore a gradient-level characterization of reverse-KL OPD trained with the K2 estimator, with SuRe as one empirical instantiation.

On-policy distillation (OPD) has emerged as a promising post-training technique for enhancing LLM reasoning. Under the reverse KL objective, the idealized optimum of OPD aligns the student distribution with that of the teacher. When the teacher consistently outperforms the student, this naturally suggests that OPD should yield broad improvements over the pre-OPD student. However, do such improvements extend across the entire range of test-time sampling budgets? In this work, we revisit this expectation through the lens of test-time scaling by varying the sampling budget K and evaluating performance with pass@K. Across multiple settings, we observe two distinct patterns: OPD can improve pass@K at both small and large sampling budgets, but it can also improve small-budget performance while reducing large-budget pass@K. We show one condition that guarantees such a reversal and an idealized reverse KL counterexample where it occurs even when the teacher has higher accuracy on every problem. To choose between two candidate teachers at a target sampling budget, we propose the Teacher Advantage Score at K (TAS@K), which can be computed before OPD training to predict which teacher will lead to a larger improvement in pass@K. Across three domains and thirteen benchmarks, the ordering predicted by TAS@K agrees with the observed pass@K improvements of the resulting OPD models in 83.6\% of experiments, providing a useful signal for teacher selection at the target pass@K.

On-policy distillation (OPD) strengthens language-model reasoning, yet whether students acquire new factual knowledge or compositional skill for multi-step reasoning remains unknown. We separate these capabilities using a controlled synthetic framework that measures the student's initial capabilities and independently controls the teacher's additional facts, compositional skill, or both. Across four models from three families, reverse-KL OPD reliably transfers compositional skill across unseen reasoning structures, but transfers minimal factual knowledge. Decoupling the distillation recipe reveals the source of this asymmetry: replacing reverse KL with forward KL restores factual transfer, whereas student rollouts specifically improve the execution of multi-step reasoning. Experiments on recent factual QA and competition mathematics show a similar asymmetry under reverse-KL OPD, yielding notable reasoning gains without factual memory expansion. Together, these results demonstrate that on-policy distillation does not expand a model's parametric knowledge, but instead teaches it to organize and compose the knowledge it already possesses.

Knowledge distillation (KD) is a widely adopted technique for transferring knowledge from large language models to smaller student models; however, conventional supervised KD often suffers from a distribution mismatch between training and inference. While on-policy KD approaches attempt to mitigate this issue by learning directly from student-generated outputs, they frequently encounter training instabilities because the distributional gap between the novice student and the expert teacher is often too wide to bridge directly. These challenges manifest as pathological gradients in forward KL objectives or diversity collapse in reverse KL regimes. To address these limitations, we propose Veto, an objective-level reformulation that constructs a geometric bridge in the logit space. Unlike prior methods that mix data samples, Veto creates an intermediate target distribution that promotes alignment between the teacher and the student. By introducing a tunable parameter beta, Veto serves as an Adaptive Gradient Veto that stabilizes optimization by suppressing harmful gradients on low-confidence tokens, while simultaneously acting as a Decisiveness Knob to balance reward-driven performance with output diversity. Extensive experiments across various reasoning and generation tasks demonstrate that Veto consistently outperforms supervised fine-tuning and existing on-policy baselines.

Context distillation enables language models to internalize in-context knowledge into their parameters. In our work, we propose On-Policy Context Distillation (OPCD), a framework that bridges on-policy distillation with context distillation by training a student model on its own generated trajectories while minimizing reverse Kullback-Leibler divergence against a context-conditioned teacher. We demonstrate the effectiveness of OPCD on two important applications: experiential knowledge distillation, where models extract and consolidate transferable knowledge from their historical solution traces, and system prompt distillation, where models internalize beneficial behaviors encoded in optimized prompts. Across mathematical reasoning, text-based games, and domain-specific tasks, OPCD consistently outperforms baseline methods, achieving higher task accuracy while better preserving out-of-distribution capabilities. We further show that OPCD enables effective cross-size distillation, where smaller student models can internalize experiential knowledge from larger teachers.

Reasoning models think out loud, but much of what they say is noise. We introduce OPSDC (On-Policy Self-Distillation for Reasoning Compression), a method that teaches models to reason more concisely by distilling their own concise behavior back into themselves. The entire approach reduces to one idea: condition the same model on a "be concise" instruction to obtain teacher logits, and minimize per-token reverse KL on the student's own rollouts. No ground-truth answers, no token budgets, no difficulty estimators. Just self-distillation. Yet this simplicity belies surprising sophistication: OPSDC automatically compresses easy problems aggressively while preserving the deliberation needed for hard ones. On Qwen3-8B and Qwen3-14B, we achieve 57-59% token reduction on MATH-500 while improving accuracy by 9-16 points absolute. On AIME 2024, the 14B model gains 10 points with 41% compression. The secret? Much of what reasoning models produce is not just redundant-it is actively harmful, compounding errors with every unnecessary token.

On-policy distillation is a promising approach for transferring knowledge between language models, where a student learns from dense token-level signals along its own trajectories. This framework typically uses reverse KL divergence, encouraging the student to match the teacher's high-confidence predictions. However, we show that the mode-seeking property of reverse KL reduces generation diversity and yields unstable learning signals when the teacher distribution has high entropy. To address this, we introduce Entropy-Aware On-Policy Distillation. Our key idea is augmenting the standard reverse KL objective with forward KL when teacher entropy is high, capturing the full range of plausible outputs while retaining precise imitation elsewhere. It balances mode-seeking precision with mode-covering robustness without sacrificing on-policy training efficiency. Experiments show that our method maintains generation diversity (sustained token-level entropy) and improves student-teacher alignment (lower forward KL on high-entropy tokens). Across six math reasoning benchmarks, this yields Pass@8 accuracy gains of +1.37 for Qwen3-0.6B-Base, +2.39 for Qwen3-1.7B-Base, and +5.05 for Qwen3-4B-Base compared to baseline on-policy distillation methods. These results demonstrate that accounting for teacher uncertainty is essential for maintaining diversity and achieving effective knowledge transfer.

On-policy distillation (OPD) provides dense teacher supervision on student-generated trajectories, but standard reverse-KL training can assign insufficient probability to other plausible continuations. Teacher entropy alone does not reveal whether uncertainty is concentrated among a few plausible next tokens or dispersed over a long probability tail, nor whether the student already represents those candidates well. Moreover, local teacher probabilities may not predict downstream success. We introduce Sparse Probing and Outcome-calibrated Targets OPD (SPOT), which addresses two coupled decisions, where to probe and what to distill, through an acquisition--exploration--exploitation procedure. During acquisition, a position-level score combines normalized teacher entropy, the probability mass captured by a small top-k candidate set, and student--teacher mismatch to allocate a limited probing budget. During exploration, SPOT evaluates teacher-proposed candidates through verifier-scored student continuations. During exploitation, these outcomes produce a closed-form, KL-regularized target that favors candidates with better downstream outcomes while remaining anchored to the teacher distribution. Extensive experiments across multiple student models and reasoning benchmarks demonstrate the effectiveness of SPOT in improving reasoning performance while balancing solution quality and coverage.

On-Policy Distillation (OPD) trains a student on its own generations using teacher feedback. With different tokenizers, comparing teacher and student predictions requires alignment at both sequence and vocabulary levels. In this paper, we examine whether expanding this alignment coverage improves learning. Across three heterogeneous teacher--student pairs on mathematical reasoning and code generation, strict 1:1 groups already cover most student-generated tokens despite substantial vocabulary mismatch. On responses sampled from the students before distillation, the shared vocabulary retains nearly all teacher and student probability mass at strictly aligned positions on average. Restricting reverse KL to a student-selected top-16 subset of the shared vocabulary at each strict position achieves accuracy comparable to full shared-vocabulary OPD, outperforming the evaluated cross-tokenizer baselines. Adding mean squared error supervision on span log-probabilities in mismatch groups gives complete supervision coverage, yet reduces accuracy. At checkpoints from training with only the strict loss, the span gradients show weak or negative directional agreement with the strict gradients and grow in magnitude relative to them. These diagnostics may help explain the accuracy drop from adding span supervision. Our findings motivate a shift from maximizing alignment coverage to prioritizing supervision reliability: compact supervision at strict positions can be more effective than broader coverage that introduces weakly aligned or conflicting training signals.

On-policy distillation (OPD) is appealing for large language model (LLM) post-training because it evaluates teacher feedback on student-generated rollouts rather than fixed teacher traces. In long-horizon settings, however, the common sampled-token variant is fragile: it reduces distribution matching to a one-token signal and becomes increasingly unreliable as rollouts drift away from prefixes the teacher commonly visits. We revisit OPD from the estimator and implementation sides. Theoretically, token-level OPD is biased relative to sequence-level reverse-KL, but it has a much tighter worst-case variance bound; our toy study shows the same tradeoff empirically, with stronger future-reward coupling producing higher gradient variance and less stable learning. Empirically, we identify three failure modes of sampled-token OPD: an imbalanced one-token signal, unreliable teacher guidance on student-generated prefixes, and distortions caused by tokenizer or special-token mismatch. We address these issues with teacher top-K local support matching, implemented as truncated reverse-KL with top-p rollout sampling and special-token masking. Across single-task math reasoning and multi-task agentic-plus-math training, this objective yields more stable optimization and better downstream performance than sampled-token OPD.

Autoregressive video generators are attractive for streaming, long-horizon, and interactive applications, but distilling strong black-box teachers into causal students remains difficult. The student must learn under its own rollout distribution, whereas practical teachers may expose only prompt-conditioned completed videos and may differ in architecture, capacity, temporal design, and sampling schedule. This interface makes supervised fine-tuning off-policy, score-based distillation inapplicable, and direct adversarial imitation too sparse for denoising-time credit assignment. We propose Adversarial Flow Distillation (AFD), an on-policy framework for heterogeneous black-box video distillation. AFD queries the teacher and rolls out the current student on the same prompts, trains a prompt-paired Bradley-Terry discriminator to estimate clean-sample teacher-student discrepancy, and converts the resulting on-policy advantage into forward-process flow-matching updates on the student's own noised states. Thus, AFD provides dense velocity-field supervision while requiring no teacher scores, latents, denoising trajectories, step alignment, or reverse-chain reinforcement learning. Experiments across two causal AR student families show that AFD consistently improves motion- and physics-sensitive generation while preserving general video quality, and ablations validate the importance of adaptive on-policy feedback and forward-process credit assignment. The method requires only clean teacher videos and student rollouts, providing a practical route for distilling proprietary or heterogeneous video generators into efficient autoregressive students.

On-policy distillation (OPD) has become a promising paradigm for reasoning-oriented post-training of large language models (LLMs), especially when combined with reinforcement learning from verifiable rewards (RLVR). Existing OPD methods rely on reverse KL (RKL)-based teacher supervision over trajectories sampled from the student policy. However, we identify a critical limitation: under large teacher--student policy divergence, RL-driven exploration often produces trajectories outside the teacher distribution, resulting in uninformative negative feedback. To address this, we propose Teacher-Guided Policy Optimization (TGPO), an on-policy reasoning distillation method that remains effective under large policy divergence settings. Rather than relying solely on evaluative supervision, TGPO uses teacher to directly guide token level generation conditioning on student-generated contexts; together with RLVR-style trajectory level rewards, TGPO steers exploration toward improved continuations. Experiments on reasoning benchmarks show that TGPO consistently outperforms existing RKL-based OPD methods and remains robust across different teacher models.

On-policy knowledge distillation transfers reasoning from large teachers to compact students, but existing approaches suffer three compounding failure modes: (i) cold-start collapse, where a fresh student assigns near-zero mass to teacher-preferred tokens; (ii) state-agnostic divergence scheduling, where time-only forward/reverse-KL interpolation ignores the student's coverage state; and (iii) binary reward sparsity, where pass/fail signals discard information from partially correct traces. We present CADENCE, a unified framework with a targeted fix for each. Its DRIFT mechanism schedules a per-token convex mixture of forward-KL and reverse-KL surrogate objectives on student-sampled trajectories (per-token surrogates, not sequence-level KL gradient estimators). Six components extend it: (A) COVA, a coverage-adaptive β schedule accelerating the forward-to-reverse transition; (B) FTB, a forking-token boost concentrating gradient at high-entropy positions via a globally-normalized entropy reference; (C) CCD, a dense reward adding numerical-proximity partial credit for incorrect-but-close traces; (D) LAP, brevity-preferential correct-rollout reinforcement; (E) EMR, an entropy-matching calibration regularizer; (F) BSD, a bootstrapped self-distillation phase. On GSM8K and MATH-500 (corrected 512-token protocol, 5 seeds, reported std), CADENCE distills a 0.5B student from a 1.5B teacher to 69.8 pm 0.5% GSM8K pass@1 (from 48.7% pretrained; 63.2% of the teacher gap closed) and to 72.1 pm 0.4% with a 3B teacher (76.2% closed), beating the strongest matched-compute label-using baseline (DRIFT+binary reward) by +4.4 pm 0.7 points. All experiments run on a single Apple Mac Studio (M-series, 64GB unified memory), showing principled distillation reaches strong reasoning quality without datacenter-scale hardware.

On-Policy Distillation (OPD) has emerged as a dominant post-training paradigm for large language models, especially for reasoning domains. However, OPD remains unstable in practice due to the high gradient variance of its single-sample Monte Carlo estimator, and recipes for stable training are still immature. We propose vOPD (On-Policy Distillation with a control variate baseline), which casts OPD as policy-gradient RL and stabilizes it by introducing a control variate baseline-canonically a value function -- from the RL literature. We show that the OPD value function admits a closed form as the per-token negative reverse KL divergence between the student and the teacher, available directly from the already-computed forward pass with no additional critic or inference. Existing stabilization methods either compute the full token-level reverse KL over the entire vocabulary, adding significant overhead, or restrict it to a top-k support, biasing the objective. vOPD instead preserves the lightweight single-sample estimator, subtracting the value function as a detached baseline to keep the gradient unbiased while reducing variance. Furthermore, we show that a top-k approximation of the baseline further lowers cost without compromising performance. Across mathematical and scientific reasoning benchmarks, vOPD consistently outperforms vanilla OPD and matches the most expensive full-vocabulary baseline, offering an efficient stabilization of On-Policy Distillation through principled RL variance reduction.

On-policy distillation (OPD) trains a student on its own rollouts guided by teacher feedback and is becoming increasingly important for large language model (LLM) post-training. Like reinforcement learning (RL), however, OPD faces an on-policy systems bottleneck, as rollouts can dominate training time for reasoning workloads. Asynchronous training pipelines can alleviate this bottleneck by decoupling rollout generation from learner updates, but doing so introduces stale-policy data. While prior work has studied stale data in asynchronous RL, its effects in OPD remain underexplored. We present the first systematic study of staleness in asynchronous OPD, focusing on a practical setting where teacher feedback is implemented through local KL losses and full-vocabulary teacher logits are too expensive to store or transfer, necessitating finite teacher-score caches. We first show that KL direction changes the stale-data problem: teacher-weighted forward KL is more robust to stale rollouts, whereas student-weighted reverse KL is vulnerable. Second, for this vulnerable reverse-KL case, we study whether methods designed to stabilize asynchronous RL can mitigate OPD staleness. In our experiments, they do not improve over a simpler OPD-specific surrogate: recomputing the reverse-KL signal under the current student at learner time. Third, we analyze how finite teacher-score caches create a bias-variance tradeoff for sparse and sampled reverse-KL OPD estimators. This motivates multi-sample Monte Carlo (MC), which preserves MC correctability while reducing one-sample variance. Finally, we present and open-source AsyncOPD, a fully asynchronous OPD training pipeline built from these estimator choices. Experiments show that AsyncOPD improves training throughput by 1.6times to 3.8times over strict synchronous training while reaching comparable accuracy.

Extending the effective context length of large language models (LLMs) remains a central challenge for real-world applications. While recent post-training methods have made progress in long-context scaling, they either rely on high-quality supervision data or sparse sequence-level rewards, leading to unstable and inefficient optimization. We propose OPSDL, an On-Policy Self-Distillation method for enhancing the Long-context capabilities of LLMs. Unlike other recent self-distillation methods that inject privileged information and rely on the model's in-context learning ability to act as a teacher, OPSDL leverages the model's own inherently strong short-context capability as a self-teacher to supervise its own generation in long-context scenarios. The model first generates responses conditioned on the full long-context, then the self-teacher provides per-token supervision signals via point-wise reverse KL divergence under the relevant extracted short-context. This dense token-level signal encourages faithful use of relevant evidence and mitigates hallucinations induced by irrelevant context. We evaluate OPSDL on long-context benchmarks across a range of models from 7B to 32B parameters. Results show consistent and substantial improvements across varying context lengths, outperforming standard post-training approaches such as SFT and DPO with higher sample efficiency. Notably, these gains are achieved without degrading general short-context performance. These findings highlight the effectiveness of OPSDL as a scalable and stable approach for long-context learning.

On-policy distillation (OPD), which aligns a student with the teacher's token-level distribution on the student's own rollouts, is an effective paradigm for transferring capabilities across LLMs. Prevailing approaches assume a teacher at least as capable as the student: they either distill a larger model into a smaller one, which fails at the frontier where no larger teacher exists, or consolidate multiple domain experts trained from a shared base, which requires costly training at the student's scale. We introduce Weak-to-Strong On-Policy Distillation (W2S-OPD), a simple yet effective OPD framework that improves the strong student by distilling from multiple weak models. W2S-OPD constructs a proxy teacher in logit space from a contrast pair of a positive and a negative model, both smaller than the student and cheap to obtain. Their logit difference isolates the capability direction, which is added to the student's own base model, yielding a proxy teacher that couples this direction while staying distributionally adjacent to the student. The student then distills it by minimizing the per-token reverse KL on its own rollouts. We instantiate the contrast pair as i) a post-RL expert against its pre-RL initialization, isolating the skill RL instills, ii) a larger against a smaller base model, isolating the capability from scale, and iii) a small base model with correct versus wrong hints, isolating the instance-level direction toward the solution. Across four math and three code benchmarks, W2S-OPD outperforms OPD, enables the student to surpass the domain teacher, and keeps improving the student even when every supervision source is weaker. Analysis shows different contrasts yield distinct signals: the post-RL and hint contrasts emphasize reasoning frameworks, while the scale contrast emphasizes the solving procedure. Our code will be available at https://github.com/Yu-Fangxu/W2S-OPD.

On-policy distillation (OPD) has emerged as an effective paradigm for transferring knowledge between language models, where a student is trained to align its next-token distribution with the teacher's along its own trajectories. To provide dense supervision at tractable cost, many works minimize the reverse Kullback-Leibler (KL) divergence between the student and teacher's normalized distributions over the teacher's top-k tokens. However, this normalized objective discards the information about tail probability: the total probability outside the teacher's top-k tokens. As a result, the optimization can steadily increase the student's tail probability and entropy, empirically degrading downstream accuracy. To address this issue, we propose Tail-Aware Top-k OPD (TA-OPD), a novel distillation method that restores the missing tail probability signal. In particular, TA-OPD minimizes the reverse KL divergence over the top-k tokens plus a tail token that carries the tail probability. In effect, TA-OPD better aligns the student's next-token distribution with the teacher's, preventing the increase in tail probability and entropy caused by top-k normalization. Extensive experiments demonstrate the superiority of TA-OPD, improving Avg@8 by up to 8.05 points on common benchmarks. Our code is available at https://github.com/HuipengHuang/TA-OPD.

Large language model training in open-ended domains lacks verifiable rewards, making task preferences difficult to formalize as effective supervision. Contexts can convey such preferences, yet provide little additional supervision once distilled into the student, motivating contexts that evolve with student performance. However, directly using evolving contexts as in-training supervision results in an unstable distillation target and conflicting distributions, requiring mechanisms to stabilize target and downweight conflicts. In this paper, we analyze the effect of contexts through a decomposition of the reverse KL objective, revealing two findings: the student is distilled toward the geometric mean of context-conditioned teachers, and the objective contains a conflict term that measures conflicts among these teachers. Based on this decomposition, we propose Flux-OPD, an OPD paradigm that uses evolving contexts as in-training supervision to capture task preferences in open-ended domains. Flux-OPD treats the differences between context-conditioned and context-free teachers as contextual difference signals, injects them as contextual corrections into the context-free teacher anchor, and weights their correction strength using the conflict term as an indicator. Experiments on open-ended tasks show that Flux-OPD outperforms existing OPD paradigms, highlighting the potential to combine teacher supervision with evolving contexts.

On-policy distillation (OPD) reduces train-test state mismatch by training a student on its own generated trajectories, but weak students may visit teacher-misaligned prefixes where supervision is less representative. We introduce SAKI (Supervision Allocation with KL-constrained Interpolation), which combines a KL-constrained teacher-guided rollout with maximal coupling and reuses realized accept/correction events to route token-level supervision. Accepted positions retain sampled-token reverse-KL supervision, while correction positions receive direct supervision on the teacher's highest-probability token. Under maximal coupling, the correction probability is exactly TV(p_t, q_t), so the same trust-region radius controls rollout deviation and upper-bounds intervention and specialized-supervision frequency. We further implement an engine-resident speculative verifier that preserves the exact-q trajectory distribution and coupling semantics while improving matched-workload rollout throughput by 4.22x. Across seven mathematical reasoning benchmarks, SAKI improves the matched teacher-guided baseline in Mean@8 and Pass@8 for both 1.7B and 0.6B students. Placement controls and fixed-prefix analysis further support correction-triggered routing as a conflict-adaptive supervision signal.

On-Policy Distillation (OPD) is a fundamental technique for efficient post-training of large language models (LLMs), with broad applications in agent learning, multi-task enhancement, and model compression. However, OPD training becomes unstable when the teacher and student distributions differ substantially, as teacher supervision on student-generated tokens may yield unreliable policy gradients and even cause optimization failure. This work addresses reliable on-policy token-level supervision through credit assignment strategies, and proposes Trust Region On-Policy Distillation, TrOPD. It features the following characteristics: 1) Trust-Region On-Policy Learning: TrOPD performs OPD only in regions where the teacher provides reliable supervision, mitigating the optimization difficulty of the K1 reverse-KL estimator under distribution mismatch. 2) Outlier Estimation: For outlier regions, we explore gradient clipping, masking, and forward-KL estimation to reduce the adverse effects of unreliable supervision. 3) Off-Policy Guidance: The student continues generation from teacher prefixes and uses forward KL to imitate off-policy guidance, encouraging on-policy exploration toward reliable regions. Experiments show that TrOPD consistently outperforms SoTA OPD baselines, including OPD, EOPD, and REOPOLD, across mathematical reasoning, code generation, and general-domain benchmarks.

Diffusion large language models (dLLMs) are a promising alternative to autoregressive generation. However, reasoning-oriented post-training for dLLMs remains challenging. Supervised fine-tuning (SFT) for dLLMs requires dense but often off-policy masked states, while reinforcement learning (RL) relies on sparse rewards or value modeling. This paper proposes trace-based on-policy distillation (TOPD), a teacher-supervised framework that transfers reasoning ability to a target dLLM without reward estimation. The key idea is to supervise a dLLM on its own denoising trajectory, focusing on the trace-aligned token decisions that form the final response. Specifically, TOPD samples on-policy diffusion trajectories from the target dLLM, obtains teacher token distributions from a teacher model on the corresponding partially denoised states, and updates the target dLLM with a token-level Reverse Kullback-Leibler (Reverse-KL) objective. This design preserves dense teacher supervision while aligning training with the model's own denoising states. On mathematical reasoning benchmarks, TOPD enables SDAR-4B-Chat to match the MATH500 accuracy of its RL-trained counterpart TraDo-4B-Instruct, with gains of +5.7 under static evaluation and +4.5 under dynamic evaluation. Compared with the RL-trained counterpart, TOPD achieves this with 4times fewer rollout rounds, corresponding to an estimated 96.0times to-accuracy model-compute speedup.

On-policy distillation (OPD) aligns a student with a teacher on trajectories sampled from the student itself, reducing the train-test state mismatch of offline distillation. The same feedback loop can nevertheless be unstable: each update changes both the policy and the states on which the next update is computed. We introduce WDL-OPD, a mixture-constrained co-training method with two trainable policies. An anchor policy generates every rollout, an auxiliary policy evaluates the same visited states, and a geometric mixture of their token distributions is matched to a frozen teacher by reverse KL. Both policies receive gradient. We show that freezing the auxiliary recovers an anchor-plus-contrast proxy target closely related to OPD^2 and W2S-OPD, whereas joint training creates branch-level degrees of freedom that a static delta cannot express. In recorded Qwen3 experiments at 1.7B and 4B scale, WDL-OPD produces the strongest student checkpoint in each of four scale-domain settings. It raises MATH500 accuracy from 0.630 to 0.685 at 4B and from 0.521 to 0.585 at 1.7B. In code generation, seven single-policy OPD configurations exhibit entropy growth or trajectory degradation, while co-training reaches independently re-evaluated development scores of 0.637 and 0.375. Because several comparisons differ in curriculum or initialization, these results support a stabilization hypothesis rather than a universal causal claim. We provide the exact training algorithm, failure evidence, and the controlled comparison matrix needed to test that hypothesis.

On-policy distillation (OPD) and on-policy self-distillation (OPSD) have emerged as promising post-training methods for large language models, offering dense token-level supervision on trajectories sampled from the model's own policy. However, existing results on their effectiveness remain mixed: while OP(S)D has shown promise in system prompt and knowledge internalization, recent studies also report instability and degradation. In this work, we present a comprehensive empirical study of when OPD and OPSD work, when they fail, and why. We find that OPD on mathematical reasoning is highly sensitive to teacher choice and loss formulation, whereas OPSD fails in our tested settings due to test-time absence of instance-specific privileged information (PI). In contrast, OPSD is effective when PI represents a shared latent rule, such as a system prompt or alignment preference. We identify three failure mechanisms: (1) distribution mismatch between teacher and student caused by conditioning on student-generated prefixes, (2) optimization instability from biased TopK reverse-KL gradients, and (3) an OPSD-specific limitation where the student learns a PI-free policy that aggregates PI-conditioned teachers, which is insufficient when PI is instance-specific. We further show that stop-gradient TopK objectives, RLVR-adapted teachers, and SFT-stabilized students mitigate these failures.

On-Policy Distillation (OPD) improves large language model reasoning by training a student model on trajectories sampled from its own policy under teacher supervision. Although OPD operates on trajectories, its learning signal remains token-level: it identifies deviations through high-loss tokens and repairs them through local reverse-KL correction. We show that this "trajectory-sampled but token-learned" mechanism cannot reliably bridge student trajectories toward teacher trajectories. About 30% of high-loss tokens fall into the low-divergence regime, indicating that many are surface-form mismatches rather than real reasoning forks. Moreover, even truly divergent tokens are difficult to repair with isolated token-level supervision, since reasoning failures often unfold as short-horizon distributional drift. We propose Trajectory-aware OPD (TOPD), which uses near-future trajectory information to identify real divergent states and distribute guidance across multiple future tokens. Experiments show that suppressing non-divergent high-loss tokens improves standard OPD from 47.8% to 48.2% average accuracy, while TOPD further improves performance to 52.2%, with gains on AIME24 from 60.0% to 63.3% and AIME25 from 46.7% to 53.3%.

On-policy distillation (OPD) accelerates post-training by providing dense token-level supervision from a frozen teacher on the student's own rollouts. Vanilla OPD applies this supervision uniformly across prompts, without checking whether the teacher is reliable for each prompt. Because reverse KL is mode-seeking, a confidently wrong teacher can induce a strong yet misleading update. Distributional proxies, such as entropy or teacher-student likelihood agreement, measure uncertainty or agreement but do not directly verify outcome correctness. We introduce Teacher-Gated On-Policy Distillation (TGOPD), built on the principle that teacher reliability should be verified at the prompt level before dense supervision is admitted. TGOPD estimates reliability from a small set of verifier-scored teacher probes and routes each prompt exclusively to dense OPD when the reliability check passes or to verifier-grounded GRPO otherwise. Across 4B and 35B students in mathematics, code, and instruction following, TGOPD outperforms Vanilla OPD in all six single-domain settings and achieves higher seven-benchmark averages at both scales under multi-domain training. By using otherwise-idle teacher capacity for reliability estimation, TGOPD also reduces teacher-side compute waste in asynchronous OPD, increasing teacher-node GPU utilization from 9.8% to 78.9% in the measured 4B single-domain run.

On-policy learning has been argued to reduce catastrophic forgetting, produce sparser parameter updates, and improve generalisation. However, existing comparisons between supervised fine-tuning and reinforcement learning vary many factors simultaneously, making the contribution of rollout policy difficult to isolate. We study the effect of rollout policy in a controlled strong-to-weak distillation setting, by independently varying rollout policy, token-level KL direction, and learning rate across the Llama3 and Qwen2.5 model families and reasoning tasks spanning scientific, medical, and arithmetic domains. Our analysis reveals a nuanced picture of distillation dynamics in which rollout policy does not necessarily play a central role. Instead, token-level KL direction more clearly shapes task performance and output coverage, while learning rate governs forgetting and update sparsity. Analysis of KL gradients and experiments along a continuous student-teacher rollout-policy spectrum explain this pattern: forward KL is remarkably robust to rollout policy, with its performance stable and strong despite changes to the rollout policy, whereas reverse KL is substantially more sensitive and favours student-generated rollouts. On-policy data nevertheless improves generalisation to harder variants of the Countdown arithmetic task under both KL directions, although this advantage does not reliably persist after subsequent RLVR. Our broader conclusions remain robust to removing gradient clipping, using sampled KL estimators, and training on tasks requiring longer reasoning chains. Overall, our results challenge the view that on-policy rollouts are inherently preferable and show that their value depends critically on the objective, evaluation setting, and optimisation hyperparameters.

On-policy distillation (OPD) transfers teacher knowledge on student-generated trajectories, but efficient sampled objectives reduce the teacher distribution to scalar credit on individual tokens. Such credit indicates whether a token should gain or lose probability, yet leaves the corresponding redistribution unspecified. We recast OPD as teacher-guided probability transport and propose RouteOPD (Routed On-Policy Distillation), which decomposes local teacher--student disagreement into student-excess sources and teacher-deficit destinations and couples them into explicit transport pairs. RouteOPD optimizes pairwise log-odds toward jointly realizable targets obtained from a bounded teacher potential, while adapting the transport budget to the concentration of teacher demand. This formulation directs updates toward teacher-preferred destinations and controls their magnitude within a single transport operator. Experiments across four teacher--student settings and four mathematical-reasoning benchmarks demonstrate that RouteOPD consistently outperforms sampled reverse-KL OPD, with improvements accompanied by higher routing fidelity and lower background leakage. These results demonstrate the effectiveness of explicitly modeling probability transport in on-policy distillation.

On-policy distillation (OPD) trains a student on prefixes sampled from its own policy while matching a stronger teacher. This addresses the prefix mismatch of offline distillation, but early student rollouts can still be poor, placing teacher supervision on weak or low-quality prefixes. We propose Trust-Region behavior Blending (TRB), a warmup method that replaces the early rollout policy with the closest-to-teacher behavior policy inside a student-centered KL trust region, while keeping the per-prefix reverse-KL OPD loss unchanged. The KL budget is annealed to zero, so training returns to pure student rollouts after warmup. Across two math-reasoning distillation settings, TRB attains the strongest average among the compared methods.

On-policy self-distillation (OPSD) enables large language models (LLMs) to learn from privileged information (PI) without a separate teacher model. However, prior work largely treats PI as a fixed design choice, leaving the effects of its content and construction poorly understood. This challenge is particularly important in multi-turn agentic settings, where trajectories contain actions, observations, and reasoning that can be transformed into PI in many ways. We systematically evaluate 16 PI configurations across three multi-turn agentic benchmarks and three student models that vary in scale and reasoning mode. We find that PI effectiveness depends on its content, generation source, and the student model. Information-dense trajectories and PI produced by more capable generators generally yield larger gains, whereas thinking models benefit less consistently. To assess PI before training, we compare PI utility with two KL-based metrics: sampled-token reverse KL (D) and error-step KL contrast (Δd^{-}_{err}). The KL-based metrics track post-training performance more consistently than PI utility, which can be distorted by information leakage. Empirically, selecting each task's PI by Δd^{-}_{err} also improves post-training performance over random selection, most when the PI candidates differ widely. Finally, effective PI remains beneficial when combined with GRPO, allowing the combined objective to outperform a strong GRPO baseline. Overall, our results provide practical guidance for constructing and evaluating PI in OPSD training.

On-policy distillation (OPD) trains a student on its own trajectories under token-level teacher supervision, but existing methods are capped by a single-teacher capability ceiling: when the teacher errs, the student inherits the error. OPD also remains largely unexplored in agentic tasks, where per-step errors compound across long trajectories and destabilize training. We propose MAD-OPD (Multi-Agent Debate-driven On-Policy Distillation), which breaks this ceiling by recasting the distillation teacher as a deliberative collective of teachers that debate over the student's on-policy state; the debate produces an emergent collective intelligence that supplies token-level supervision, with each teacher's contribution weighted by its post-debate confidence. To extend OPD to agentic tasks, we also introduce On-Policy Agentic Distillation (OPAD), which adds step-level sampling to stabilize training under multi-step error compounding. We additionally derive a task-adaptive divergence principle, selecting JSD (Jensen-Shannon divergence) for agentic stability and reverse KL (Kullback-Leibler) divergence for code generation, and verify it both theoretically and empirically. Across six teacher-student configurations (Qwen3 and Qwen3.5; 1.7B-14B students, 8B-32B teachers) and five agentic and code benchmarks, MAD-OPD ranks first across all six configurations; on the 14B+8Bto4B setting it lifts the agentic average by +2.4% and the code average by +3.7% over the stronger single-teacher OPD.

Since the advent of knowledge distillation, KL divergence has been the standard loss in distillation. Recently, on-policy distillation (OPD) has emerged as an efficient post-training paradigm for LLMs. As a distillation method, OPD naturally inherits KL divergence as its standard loss. However, in this work, we find that KL divergence may not be necessary for OPD. We show that simply preserving the update direction is sufficient for effective OPD. As long as the update direction is toward the teacher, OPD works. More precisely, it is not the direction of every token, but the direction of a small subset of tokens where the teacher and student disagree strongly. We first show that simply assigning a reward of (+1) to tokens where the teacher probability is higher than the student probability and (-1) where it is lower, which merely encourages updates toward the teacher, reproduces almost the same training mode as OPD with reverse KL. We further show that only the direction of a small subset of tokens with large teacher-student disagreement is critical, and training works as long as their update direction is toward the teacher, even if other tokens are pulled away from the teacher. And as an application of these findings, we introduce Consensus Multi-Teacher On-Policy Distillation (C-MOPD) to improve Multi-Teacher On-Policy Distillation (MOPD). Unlike MOPD, which routes each sample to a single teacher and may cause capability conflicts across domains, C-MOPD lets every sample be supervised by all teachers. Experiments show that C-MOPD consistently outperforms MOPD on both math and code benchmarks. Our code is available at https://github.com/LeapLabTHU/KL-Free-OPD.

*Reinforcement learning (RL)* can induce substantial reasoning capabilities in large language models (LLMs), but how much of this capability transfers across model scales, and how quickly, remains unclear. We study the scaling properties of *on-policy distillation (OPD)* across *weak-to-strong*, *same-base*, and *strong-to-weak* teacher--student setups. We find that early OPD training dynamics uniformly exhibit a regular *useful-transfer* regime, in which held-out accuracy (the *gold score*, G) rises approximately linearly in d=mathrm{KL(π_θVert π_{ref})}, the square root of token-level reverse KL divergence from the student initialization. In every observed weak-to-strong pair, the student's peak gold score exceeds its teacher's own, so a compact RL expert can transfer capability to a much larger student via OPD. To estimate OPD outcomes, we fit *power laws* for how G_{peak} and the slope of the useful-transfer regime scale with student and teacher parameter counts and with teacher gold score. These laws show that peak gold score improves with teacher scale only up to roughly the student's scale, and that at a matched gold score smaller teachers transfer better, so a teacher's score alone does not define its supervision value. We also study the scaling effects of two OPD variants, bootstrapping weak-to-strong OPD, and the degree of on-policy supervision.

On-policy distillation (OPD) trains students using teacher feedback on their own sampled responses, yet how prompt choice shapes transfer across teacher-student pairs remains poorly understood. We systematically study prompt quantity, source, and selection across RL- and SFT-continuation pairs and cross-model settings. We find that OPD can be highly prompt-efficient: a few prompts can approach large-pool performance, with four DAPO prompts matching the observed mathematics score of 3,840 DeepMath prompts. However, prompt utility is relational rather than intrinsic: changing only the teacher can reverse the relative effectiveness of mathematics and code prompts. To characterize these transfer differences, we analyze parameter and functional changes across prompt supports and model pairs. Functional alignment with the teacher varies across supports and target tasks; in continuation pairs, teacher-aligned prediction changes can coexist with weak parameter alignment. Continued OPD on effective supports can restore performance after unfavorable transfer. Finally, targeted selection does not consistently outperform uniform random sampling, and filtering out a source that performs poorly alone yields no consistent gain across three paired support draws. Overall, our results distinguish prompt efficiency from prompt interchangeability and show that effective data choice depends on the teacher-student pair and target capability, with random sampling providing a competitive baseline in the studied settings.

Sparse on-policy distillation (OPD) allocates teacher supervision to a small subset of tokens in student-generated trajectories. However, useful teacher guidance can yield a noisy update when its gradient is estimated from a sampled next token. We study this estimation problem at a fixed prefix in information geometry and propose an information-efficiency ratio (IER) based on a signal-to-noise decomposition. IER characterizes relative gradient estimation error under an optimal scalar baseline. A candidate-set approximation enables token selection based on IER and its combination with existing usefulness scores, while retaining the sampled reverse-KL training objective. On mathematical and medical reasoning tasks, adding IER improves existing selectors in multiple settings, with sparse configurations matching or exceeding full OPD without token selection at small token budgets of 0.1\%--1\%. These results support accounting for both usefulness and gradient-estimation reliability when allocating sparse supervision. Our code is available at https://github.com/BruceSheng1202/IER-OPD.

Reinforcement learning has emerged as a principled post-training paradigm for Temporal Video Grounding (TVG) due to its on-policy optimization, yet existing GRPO-based methods remain fundamentally constrained by sparse reward signals and substantial computational overhead. We propose Video-OPD, an efficient post-training framework for TVG inspired by recent advances in on-policy distillation. Video-OPD optimizes trajectories sampled directly from the current policy, thereby preserving alignment between training and inference distributions, while a frontier teacher supplies dense, token-level supervision via a reverse KL divergence objective. This formulation preserves the on-policy property critical for mitigating distributional shift, while converting sparse, episode-level feedback into fine-grained, step-wise learning signals. Building on Video-OPD, we introduce Teacher-Validated Disagreement Focusing (TVDF), a lightweight training curriculum that iteratively prioritizes trajectories that are both teacher-reliable and maximally informative for the student, thereby improving training efficiency. Empirical results demonstrate that Video-OPD consistently outperforms GRPO while achieving substantially faster convergence and lower computational cost, establishing on-policy distillation as an effective alternative to conventional reinforcement learning for TVG.

Large language model post-training methods such as supervised fine-tuning (SFT), reinforcement learning (RL), and distillation are often analyzed through their loss functions: maximum likelihood, policy gradients, forward KL, reverse KL, or related objective-level variants. We study a complementary factor: the state distribution on which supervision is applied. For an autoregressive policy, a state is a prompt plus generated prefix. SFT trains on fixed dataset states, while RL and on-policy distillation (OPD) train on states induced by the current learner. We formalize post-training as state-distribution shaping and run a controlled smallscale study using Qwen3-0.6B-Base on GSM8K, with TruthfulQA and MMLU as retention evaluations. Our results show three phenomena. First, a mild SFT run improves GSM8K with little forgetting, while a stress SFT run causes substantial retention loss. Second, OPD from a degraded SFT teacher surpasses that teacher on GSM8K, TruthfulQA, and MMLU, despite using the teacher as its only supervision source. Third, a lightweight on-policy RL run improves GSM8K while preserving retention. These results support a state-centric view of post-training: the source and locality of training states can be as important as the form of the supervision signal.

We study on-policy distillation (OPD) through the lens of reinforcement learning, establishing a connection between the reverse-KL objective in OPD and KL-regularized policy optimization. Building on this connection, we introduce Least-Square Policy Distillation (LSPD), an RL-inspired framework that brings optimistic exploration and off-policy data reuse from value-based RL into policy distillation. LSPD preserves policy diversity through exploration while improving rollout efficiency by repeatedly learning from previously collected trajectories. Our theoretical analysis connects LSPD to optimistic value-based learning and shows that its idealized formulation achieves a sharp mathcal O(log K) regret bound under online exploration. Empirically, LSPD consistently outperforms existing distillation baselines across six mathematical reasoning benchmarks and diverse teacher-student settings, with average gains of +1.59 points in Avg@16. Remarkably, through Pass@k evaluations up to k=64, we found that LSPD better preserves policy diversity by achieving stronger performance as k grows. Its fully off-policy variant achieves comparable performance to vanilla OPD using only the first 25% of rollout batches. Together, these results provide an RL perspective on OPD that offers both a principled interpretation and a practical route toward more effective and rollout-efficient language model distillation.

Knowledge distillation (KD) is a powerful paradigm for compressing large language models (LLMs), whose effectiveness depends on intertwined choices of divergence direction, optimization strategy, and data regime. We break down the design of existing KD methods and present a unified view that establishes connections between them, reformulating KD as a reweighted log-likelihood objective at the token level. We further propose Hybrid Policy Distillation (HPD), which integrates the complementary advantages of forward and reverse KL to balance mode coverage and mode-seeking, and combines off-policy data with lightweight, approximate on-policy sampling. We validate HPD on long-generation math reasoning as well as short-generation dialogue and code tasks, demonstrating improved optimization stability, computational efficiency, and final performance across diverse model families and scales. The code related to this work is available at https://github.com/zwhong714/Hybrid-Policy-Distillation.

Speculative decoding, in which a lightweight draft model first generates a draft sequence that is then verified in parallel by the target model, has become a prevalent paradigm for accelerating large language model inference. Recent work such as DFlash further boosts drafting efficiency by leveraging diffusion drafters, whose parallel denoising mechanism enables draft generation in a single forward pass. In this work, we uncover a central pitfall of diffusion drafters: bidirectional attention is a double-edged sword. On one hand, it endows the model with parallel generation and global contextual modeling capabilities; on the other hand, this inherent global dependency introduces high variance at both the domain-level and the token-level: acceptance rates fluctuate substantially across different domains, and draft token quality also varies heterogeneously at different token positions. To tackle this issue, we propose AdaFlash framework, comprising two components: (i) an on-policy distillation (OPD) algorithm with reverse-KL divergence tailored for diffusion drafters, bringing stable convergence and effectively reducing domain-level variance; and (ii) an adaptive length head that dynamically adjusts the candidate sequence length on the fly, substantially lowering the verification cost of the target model and handling token-level variance. Experiments demonstrate that AdaFlash consistently improves speedup rate during deployment, with especially significant gains in high-concurrency scenarios, achieving up to approximately 66% higher throughput than previous state-of-the-art methods.

Multi-teacher on-policy distillation (MOPD) distills several domain-expert teachers into a single student by minimizing per-domain reverse-KL divergence on the student's own rollouts. Existing approaches typically fix the per-domain data mixture before training, overlooking the fact that different domains converge at substantially different rates: some plateau early while others continue to improve throughout the training budget. A fixed mixture therefore wastes compute on fast-converging domains and undertrains slower-converging ones. To address this, we propose D^3-MOPD (Dynamic Domain ScheDuling for MOPD), a zero-overhead scheduler that repurposes the per-domain reverse-KL signal already produced during training to adapt the domain mixture online. Running asynchronously outside the training process, an off-process watcher periodically tracks each domain's KL trajectory, estimates remaining headroom and current improvement rate, and accordingly adjusts the domain sampling ratios without altering the core training loop. Our D^3-MOPD scales naturally to arbitrary numbers of domains, and the expected benefit grows as more domains introduce more diverse convergence patterns for the scheduler to exploit. On a Qwen3.6-35B-A3B student distilled from four domain-expert teachers, D^3-MOPD closes 97% of the average student-to-teacher performance gap, compared with 63% for vanilla MOPD, reaches the same peak performance with an approximately 3times reduction in rollout steps, and surpasses the specialist teachers on three of seven benchmarks.

Training-time privileged information (PI) can enable language models to succeed on tasks they would otherwise fail, making it a powerful tool for reinforcement learning in hard, long-horizon settings. However, transferring capabilities learned with PI to policies that must act without it at inference time remains a fundamental challenge. We study this problem in the context of distilling frontier models for multi-turn agentic environments, where closed-source systems typically hide their internal reasoning and expose only action trajectories. This breaks standard distillation pipelines, since successful behavior is observable but the reasoning process is not. For this, we introduce π-Distill, a joint teacher-student objective that trains a PI-conditioned teacher and an unconditioned student simultaneously using the same model. Additionally, we also introduce On-Policy Self-Distillation (OPSD), an alternative approach that trains using Reinforcement Learning (RL) with a reverse KL-penalty between the student and the PI-conditioned teacher. We show that both of these algorithms effectively distill frontier agents using action-only PI. Specifically we find that π-Distill and in some cases OPSD, outperform industry standard practices (Supervised finetuning followed by RL) that assume access to full Chain-of-Thought supervision across multiple agentic benchmarks, models, and forms of PI. We complement our results with extensive analysis that characterizes the factors enabling effective learning with PI, focusing primarily on π-Distill and characterizing when OPSD is competitive.

Autoregressive video diffusion with causal diffusion transformers has emerged as a major paradigm for real-time streaming video generation and action-conditioned interactive world models. In this work, we extend rCM, an advanced diffusion distillation framework, to autoregressive video diffusion. The core philosophy of rCM lies in the complementarity between forward and reverse divergences, represented by consistency models (CMs) and distribution matching distillation (DMD), respectively, in diffusion distillation. This philosophy naturally carries over to the autoregressive setting, where teacher-forcing (TF) provides an offline, forward-divergence causal training paradigm, while self-forcing (SF) corresponds to an on-policy, reverse-divergence refinement. Our contributions are: (1) through extensive experiments, we show that teacher-forcing CM is currently the best complement to self-forcing DMD as an initialization strategy (2) we present the first implementation of teacher-forcing-based continuous-time CMs (e.g., sCM/MeanFlow) for autoregressive video diffusion, enabled by our custom-mask FlashAttention-2 JVP kernel, achieving 10times faster convergence compared to discrete-time CMs (dCMs) (3) we introduce Causal-rCM, a leading, unified, and scalable algorithm-infrastructure open recipe for diffusion distillation and causal training (4) we achieve state-of-the-art streaming video generation performance in both frame-wise and chunk-wise settings, using only synthetic data for training. Notably, our distilled 2-step causal Wan2.1-1.3B model achieves a VBench-T2V score of 84.63 with only 1 or 2 sampling steps. We further apply Causal-rCM to Cosmos 3, an advanced omnimodal world foundation model for physical AI with action-conditioned generation capability, enabling an interactive world model.

Knowledge distillation is central to LLM post-training, yet its design space remains poorly understood, especially alongside reinforcement learning (RL). We show that the prevailing paradigms, off-policy distillation and on-policy distillation (OPD), implicitly couple two orthogonal choices: prefix source and token-level KL direction. This follows from decomposing sequence-level KL over autoregressive response distributions: forward KL pairs teacher prefixes with token-level forward KL, and reverse KL pairs student prefixes with token-level reverse KL. We argue this coupling is not intrinsic: decoupling the two axes yields four valid objectives. We establish gradient-level identities showing forward KL gives SFT-style cross-entropy matching with teacher soft targets, whereas reverse KL gives an RL-style policy-gradient objective with a dense teacher-student log-ratio reward, connecting them to off-policy SFT, DAgger-style on-policy SFT, offline-RL-style distillation, and OPD. We conduct an extensive controlled study on math reasoning, evaluating the four objectives both as standalone methods and as initializations for subsequent RL. The results reveal three tradeoffs: KL direction induces an accuracy-entropy tradeoff, prefix source a quality-compute tradeoff, and training length an accuracy-stability tradeoff. Motivated by these findings, we propose KL mixing and an entropy-gated length curriculum. KL mixing shows long-sequence distillation requires substantial forward-KL weight to prevent entropy collapse and length inflation without sacrificing accuracy. The entropy-gated length curriculum improves Avg@k and Pass@k by 3.6 and up to 5.8 points, and cuts average response length by roughly 3x versus fixed long-horizon training. Our results provide a framework and practical methods for designing reasoning distillation objectives that balance accuracy, diversity, compute, and RL behavior.

We present Mach-Mind-4-Flash, a 35B-parameter Mixture-of-Experts (MoE) agentic model with 3B activated parameters. Through post-training optimization alone without scaling pre-training compute, the model achieves performance on par with or surpassing that of 100B-parameter-class models. By introducing scalable agentic interaction environments for large-scale reinforcement learning, the model attains significant performance gains on real-world application tasks. Our pipeline comprises three stages: (1) a unified RL/OPD training infrastructure with dynamic multi-teacher scheduling and operator-level acceleration, delivering 17\% end-to-end training speedup; (2) multiple domain-specific RL experts trained in parallel across Reasoning, General, and Agent tracks, then fused into a single generalist via Multi-Teacher On-Policy Distillation (MOPD) -- a routed reverse-KL objective that eliminates the see-saw degradation of mixed-reward RL; (3) Hybrid Median-length Policy Optimization (HMPO), a single-stage token-efficiency method that compresses reasoning chains by 19--46\% with le0.7 percentage-point accuracy loss. Mach-Mind-4-Flash scores 92.70 on AIME'26, 82.82 on IFBench, 80.74 on Behavioral-SafetyBench, 75.80 on BFCL-v4, 72.31 on BrowseComp-zh, and 84.20 on ClawBench -- leading or matching models with 10--30times its activated size at a fraction of the inference cost.

Reinforcement learning with outcome-based objectives such as GRPO enables LLM-based agents to solve complex, long-horizon tasks, yet the reusable exploration patterns embedded in interaction trajectories are largely discarded after a single policy update. Existing experience-augmented approaches retrieve historical guidance at inference time, but they apply experiences without accounting for the policy's evolving capability and create persistent dependencies on external retrieval. We propose EDGE (Experience-Distillation for Guided Exploration), a framework that treats retrieved experiences as temporary training-time scaffolds and progressively internalizes their benefits into the parametric policy. Concretely, EDGE partitions each rollout group into experience-conditioned and experience-free trajectories to estimate and admit only positive marginal gains without extra sampling, then distills the induced behavior into the base policy via a reverse-KL objective on its own empirical support. A co-evolutionary experience bank further synthesizes guidance from emerging failure modes and prunes obsolete entries as the policy evolves. Across embodied, web, and search-based QA tasks, EDGE improves over strong RL baselines by up to 12.5 points and remains effective without inference-time scaffolds or a proprietary reflector. The code is available at https://github.com/xvolcano02/EDGE.

In modern large language models (LLMs), LLM alignment is of crucial importance and is typically achieved through methods such as reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO). However, in most existing methods for LLM alignment, all tokens in the response are optimized using a sparse, response-level reward or preference annotation. The ignorance of token-level rewards may erroneously punish high-quality tokens or encourage low-quality tokens, resulting in suboptimal performance and slow convergence speed. To address this issue, we propose AlignDistil, an RLHF-equivalent distillation method for token-level reward optimization. Specifically, we introduce the reward learned by DPO into the RLHF objective and theoretically prove the equivalence between this objective and a token-level distillation process, where the teacher distribution linearly combines the logits from the DPO model and a reference model. On this basis, we further bridge the accuracy gap between the reward from the DPO model and the pure reward model, by building a contrastive DPO reward with a normal and a reverse DPO model. Moreover, to avoid under- and over-optimization on different tokens, we design a token adaptive logit extrapolation mechanism to construct an appropriate teacher distribution for each token. Experimental results demonstrate the superiority of our AlignDistil over existing methods and showcase fast convergence due to its token-level distributional reward optimization.

Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow: sample many responses and reward each with a single bit indicating whether the final answer is correct. Yet many settings provide rich feedback, including execution traces, tool outputs, expert corrections, and model self-evaluations. We study how to use such feedback through a distributional variant of the classic imitation learning algorithm DAgger, where the learner has local access to an expert distribution on states visited by the current policy. This yields a simple forward cross-entropy objective that admits a blackbox expert and whose sequence-level gradient {conduct rich credit assignment by propagating} future expert-student disagreement back to earlier decisions. We show that prior RL with self-distillation objectives based on reverse KL or Jensen-Shannon fail to guarantee monotonic policy improvement: even when the expert has higher reward, their updates may increase probability on worse actions. In contrast, we show that forward cross-entropy admits monotonic policy improvement and enjoys guarantees on regret. We further show that our objective optimizes a lower bound on teacher-weighted likelihood of success, leading to improved Pass@N. Empirically, our approach, DistIL, improves over RLVR and RL with self-distillation baselines across a variety of domains: scientific reasoning, coding, and solving hard mathematical problems.

On-policy self-distillation (OPSD) trains a student on its own generated responses using feedback from the same model conditioned on privileged information. On mathematical reasoning, the original OPSD study finds that stylistic tokens can dominate the training signal over math-related tokens, and that pointwise clipping of the forward KL objective stabilizes training. Pointwise clipping caps each vocabulary-wise forward KL term at a fixed threshold before summing over the vocabulary. Follow-up studies have adopted this clipping, but its effect on training has not been directly examined. In matched training runs differing only in whether clipping is applied, we observe that clipped runs produce substantially more repetitions that persist to the end of the response than their unclipped counterparts. We trace this failure to the clipped objective. We prove that the clipped objective can fail to correct the student toward the teacher and can instead push clipped and unclipped token probabilities away from its teacher. Our training runs agree with this analysis: inside repetitions, the clipped student places less probability than its teacher on leaving the repetition, and more on continuing it, whereas the unclipped runs stay close to their teachers.

Self-distillation is a promising recipe for self-improvement in language models. In this setting, a model can serve as its own teacher when given privileged information, such as a solution to a math problem. This seems especially appealing for thinking models, which can use test-time reasoning to absorb the privileged information. Surprisingly, we show that privileged self-distillation degrades thinking models on long reasoning traces: across five Qwen3 and OLMo thinking models evaluated on AIME24, AIME25, and HMMT25, privileged-context distillation causes a relative drop of up to 17% in avg@16 accuracy. The degradation scales with the amount of privileged context withheld from the student and is most pronounced at long rollout budgets, where thinking models otherwise obtain their largest gains. This failure mode is not specific to self-distillation: on-policy distillation (OPD) improves thinking models, but privileged OPD reverses these gains. Our diagnostics link this failure mode to how privileged teacher context reshapes learning at high-entropy forking positions, where multiple continuations remain plausible and may lead to different reasoning paths. Privileged context lowers fork rates in thinking-model rollouts but not in instruction-model rollouts. This leads to an interesting dichotomy, where privileged context can help instruction-tuned models but hurts stronger thinking models. The effect is visible when the student begins a self-correction branch, where privileged OPD penalizes sampled reconsideration tokens that vanilla OPD supports. Thinking models trained with a privileged teacher produce fewer verification, backtracking, and hedging markers, even after length normalization. These findings indicate that self-distillation for strong thinking models requires attention to token-level signal, especially around correction and reasoning steps.

In on-policy distillation (OPD), the student determines which states receive teacher supervision. As its policy evolves, earlier response prefixes become less likely even though teacher-student disagreement on them persists. Under matched trajectory and optimization budgets, neither more queries nor more frequent rollout resampling is uniformly beneficial. Current-policy rollouts outperform initial-policy rollouts at shorter response budgets, but this ranking reverses at longer budgets. Replaying initial-policy rollouts after current-policy training improves accuracy, whereas replaying fixed recent rollouts does not reproduce the gain. We propose R-OPD, a gradient-triggered curriculum that adaptively selects when to revisit initial-student trajectories. When changes in mean gradients fall within minibatch-level variation for two consecutive comparisons, training switches from the next iteration onward to initial-policy replay. Across eight mathematics benchmarks and three training-data orders, R-OPD improves average accuracy over continued current-policy sampling by 2.25/4.44 percentage points at 16K/32K for a 0.6B student and 2.81/6.15 points for a 1.7B student. With a 30B-A3B teacher, it improves 8B accuracy by 4.05 points at 32K. At 32K, R-OPD exceeds a fixed schedule of 40 current-policy updates followed by 20 replay updates by 1.39/1.66/1.85 points for 0.6B/1.7B/8B. At the same generation cap, R-OPD also produces longer responses, suggesting that well-timed revisits help students use more of their reasoning capacity.

On-policy distillation is pivotal for transferring reasoning capabilities to capacity-constrained models, yet remains prone to instability and negative transfer. We show that on-policy distillation can be interpreted, both theoretically and empirically, as a form of policy optimization, where the teacher-student log-likelihood ratio acts as a token reward. From this insight, we introduce REOPOLD (Relaxed On-Policy Distillation) a framework that stabilizes optimization by relaxing the strict imitation constraints of standard on-policy distillation. Specifically, REOPOLD temperately and selectively leverages rewards from the teacher through mixture-based reward clipping, entropy-based token-level dynamic sampling, and a unified exploration-to-refinement training strategy. Empirically, REOPOLD surpasses its baselines with superior sample efficiency during training and enhanced test-time scaling at inference, across mathematical, visual, and agentic tool-use reasoning tasks. Specifically, REOPOLD outperforms recent RL approaches achieving 6.7~12x greater sample efficiency and enables a 7B student to match a 32B teacher in visual reasoning with a ~3.32x inference speedup.

On-policy distillation (OPD) trains a student on its own trajectories with token-level teacher feedback and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its standard advantage weighted policy gradient suffers from three structural weaknesses, including high variance updates, vanishing gradients in zero-advantage regions, and exploration bottlenecks when corrective signals are insufficient. We therefore propose Asymmetric On-Policy Distillation (AOPD), which replaces ineffective negative reinforcement with localized divergence minimization in non-positive advantage regions while preserving positive reinforcement learning. Experiments on mathematical reasoning benchmarks show that AOPD consistently outperforms standard OPD, with average gains of 4.09 / 8.34 under strong / weak initialization, respectively. AOPD also maintains higher policy entropy during training and better capability retention during sequential tool-use adaptation.

On-policy distillation (OPD), which samples trajectories from the student model and supervises them with a teacher at the token level, avoids relying solely on verifiable terminal rewards and can yield better generalization than off-policy distillation. However, OPD requires expensive on-the-fly sampling of the student policy during training, which substantially increases training cost, especially for long responses. Our initial analysis shows that, during OPD, training signals are often concentrated in the prefix of each output, and that even a short teacher-generated prefix can significantly help the student produce the correct answer. Motivated by these observations, we propose a simple yet effective modification of OPD: we apply the distillation objective only to prefixes of student-generated outputs and terminate each sampling early during distillation. Experiments on a suite of AI-for-Math and out-of-domain benchmarks show that on-policy prefix distillation matches the performance of full OPD while reducing training FLOP by 2x-47x.

On-policy distillation is an alternative post-training method in reinforcement learning that alleviates the constraints imposed by reward models by providing token-level supervision from a teacher model. Although on-policy distillation has been studied and applied across various settings, its fundamental design remains underexplored. In this paper, we introduce a new distillation reward, termed the delta signal, instead of directly imitating the teacher's output distribution. The delta signal is defined as the difference between the teacher model and its base model prior to instruction tuning for reasoning capability. It therefore captures the changes induced by reasoning tuning and provides a more direct signal for transferring reasoning capabilities. Using extensive empirical evidence, we show that the delta signal substantially improves on-policy distillation and refer to the new distillation method as On-Policy Delta Distillation (OPD^2). Experiments across mathematics, science, and code-reasoning benchmarks demonstrate that OPD^2 consistently outperforms conventional on-policy distillation, enabling reasoning LLMs to achieve strong performance with only a short post-training period. Code will be available at https://github.com/naver-ai/opd2

Knowledge distillation has become a primary mechanism for transferring reasoning and domain expertise from frontier Large Language Models (LLMs) to smaller, deployable students. However, the dominant paradigm remains off-policy: students train on static teacher-generated data and never encounter their own errors during learning. This train--test mismatch, an instance of exposure bias, causes prediction errors to compound autoregressively at inference time. On-Policy Distillation (OPD) addresses this by letting the student generate its own trajectories and receive teacher feedback on these self-generated outputs, grounding distillation in the theory of interactive imitation learning. Despite rapid growth spanning divergence minimization, reward-guided learning, and self-play, the OPD literature remains fragmented with no unified treatment. This survey provides the first comprehensive overview of OPD for LLMs. We introduce a unified f-divergence framework over on-policy samples and organize the landscape along three orthogonal dimensions: feedback signal (logit-based, outcome-based, or self-play), teacher access (white-box, black-box, or teacher-free), and loss granularity (token-level, sequence-level, or hybrid). We systematically analyze representative methods, examine industrial deployments, and identify open problems including distillation scaling laws, uncertainty-aware feedback, and agent-level distillation.

On-policy distillation has been widely adopted for alleviating the distribution mismatch of off-policy distillation. Self-distillation further removes the need for an external teacher by using the student's own outputs, enhanced with extra context or demonstrations, as supervision. This teacher-free design makes on-policy self-distillation practical, yet its privacy risks remain largely unexplored. In particular, using two coupled views of the same training example may strengthen its memorization. Motivated by this, we present the first study of membership inference attacks against on-policy self-distillation. We investigate both gray-box and black-box threat models and propose a unified attack framework, named OP-Print. OP-Print builds on our finding that the supervision imprint in on-policy self-distillation is sparse and structured, concentrating on uncertainty-sensitive correction sites rather than across the entire rollout. Exploiting this property, we construct attack signals tailored to the two access levels: in the gray-box setting, OP-Print directly aggregates the privileged teacher-student residual correction along the same rollout; in the black-box setting, it measures restart-based output-basin stability as an observable surrogate for the hidden correction process. Across diverse models and distillation schemes, all baseline attacks remain essentially at random guessing even under gray-box access, whereas OP-Print is broadly validated to be effective in both gray-box and black-box settings.

On-policy distillation (OPD) has been widely studied as a post-training method in which a student model obtains token-level supervision from a stronger teacher on its own rollouts. Recent studies have improved OPD through alternative distillation reward formulations and teacher configurations, while the objective of distillation remains centered on mimicking the teacher. However, when a stronger teacher has limited distributional overlap with the student, such positive guidance can provide insufficient learning signals. In this work, we introduce Negative-Policy OPD (NP-OPD), which complements teacher supervision with rollouts from a lower-performing, lower-capability negative policy that serves as a negative reference for the student. Rather than modifying the distillation reward formulation, NP-OPD introduces the negative policy at the rollout stage, continuously supplying tokens preferred by the negative policy over the teacher so that they remain exposed to teacher supervision throughout training. This provides an explicit negative signal through negative-policy rollouts while preserving the positive teacher supervision used in OPD. Through extensive experiments, we show that NP-OPD improves OPD across model scales, generation modes, reasoning domains, and different OPD variants. Furthermore, our analyses show that NP-OPD effectively suppresses tokens preferred by the negative policy over the teacher and moves the student away from the negative policy. These results support our design of introducing negative signals through negative-policy rollouts and provide new insight into the role of the rollout policy in OPD. Code will be available at https://github.com/naver-ai/np-opd.

Knowledge distillation improves large language model (LLM) reasoning by compressing the knowledge of a teacher LLM to train smaller LLMs. On-policy distillation advances this approach by having the student sample its own trajectories while a teacher LLM provides dense token-level supervision, addressing the distribution mismatch between training and inference in off-policy distillation methods. However, on-policy distillation typically requires a separate, often larger, teacher LLM and does not explicitly leverage ground-truth solutions available in reasoning datasets. Inspired by the intuition that a sufficiently capable LLM can rationalize external privileged reasoning traces and teach its weaker self (i.e., the version without access to privileged information), we introduce On-Policy Self-Distillation (OPSD), a framework where a single model acts as both teacher and student by conditioning on different contexts. The teacher policy conditions on privileged information (e.g., verified reasoning traces) while the student policy sees only the question; training minimizes the per-token divergence between these distributions over the student's own rollouts. We demonstrate the efficacy of our method on multiple mathematical reasoning benchmarks, achieving 4-8x token efficiency compared to reinforcement learning methods such as GRPO and superior performance over off-policy distillation methods.

On-policy distillation (OPD) trains a student on its own trajectories with dense per-token supervision from a stronger teacher, and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its effectiveness implicitly relies on two assumptions that frequently break in practice: trajectory-level alignment between the student and the teacher, and uniform token-level reliability of the teacher's preferences. We therefore propose Sign-Gated On-Policy Distillation (SG-OPD), which uses a binary verifier as a trust signal for the teacher at two complementary granularities: phased teacher sampling mixes in verifier-endorsed teacher rollouts at cold-start, and a sign-consistency gate extrapolates the distillation update on tokens where the teacher agrees with the verifier-correct direction and interpolates it where it disagrees. Experiments on competition-level mathematical reasoning benchmarks show that SG-OPD consistently outperforms standard OPD, with average gains of 1.98 and 7.50 at the per-sample and per-question levels, respectively.

On-policy distillation (OPD) improves language-model by supervising a student on prefixes sampled from its own policy, but its supervision remains confined to the output space. Consequently, OPD transfers what a teacher predicts without supervising the intermediate computation that produces those predictions. Simply distilling intermediate representations like representation matching is insufficient since teacher and student representations may differ geometrically, and even well-aligned hidden states need not be usable by the student's subsequent computation. We introduce On-Policy Mechanism Distillation (OPMD), which transfers teacher-derived intermediate computation while explicitly accounting for its compatibility with the student. OPMD first constructs a student-compatible teacher that transforms teacher representations into intermediate states usable by the student's downstream computation, then it internalizes these states from on-policy trajectories. OPMD achieves the highest average accuracy among the evaluated distillation baselines in all three teacher--student settings, and generalizes to multi-teacher distillation and cross-family supervised fine-tuning. Further analyses show that mechanism supervision yields more effective reasoning and meaningfully alters the student's intermediate computation and solution strategies, supporting that it transfers information beyond output supervision alone. Together, these results establish mechanism-level supervision as an effective way to move on-policy distillation beyond output supervision, enabling students to learn inner mechanisms they can use and internalize.

Off-policy and on-policy distillation have traditionally been formulated as separate paradigms, each favoring a different property of distillation trajectories. Teacher-generated (off-policy) traces are typically high-quality but lie far from the student's distribution, whereas student-generated (on-policy) rollouts are more learnable but often contain erroneous reasoning. We view these paradigms as the endpoints of a policy continuum and posit that a more effective rollout policy may lie in between. We introduce Interpolated Policy Distillation (IPD), which defines the next-token distribution at every decoding step as an explicit linear interpolation between the student and teacher distributions. The interpolation operates at the distribution level, token by token, and its coefficient provides direct control over the balance between trajectory quality and student learnability. Naively sampling from this policy would require sequentially querying the teacher at every token and is thus expensive. To make IPD practical, we accelerate it with a new speculative-decoding rule while exactly preserving the interpolated next-token distribution.At the trajectory level, the resulting rollouts naturally interleave student- and teacher-generated segments. Unlike recent heuristic segment-interleaving methods, however, this interleaving is induced by an exactly realized token-level interpolated policy rather than by hand-designed switching rules. Across text-only and multimodal reasoning benchmarks, IPD consistently outperforms both endpoint policies (SFT and OPD), their conventional two-stage combination (SFT-then-OPD), and recent heuristic segment-interleaving methods, demonstrating that token-level policy interpolation better balances trajectory quality and student learnability.

On-policy distillation (OPD) has recently emerged as an effective post-training paradigm for consolidating the capabilities of specialized expert models into a single student model. Despite its empirical success, the conditions under which OPD yields reliable improvement remain poorly understood. In this work, we identify two fundamental bottlenecks that limit effective OPD: insufficient exploration of informative states and unreliable teacher supervision for student rollouts. Building on this insight, we propose Uni-OPD, a unified OPD framework that generalizes across Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs), centered on a dual-perspective optimization strategy. Specifically, from the student's perspective, we adopt two data balancing strategies to promote exploration of informative student-generated states during training. From the teacher's perspective, we show that reliable supervision hinges on whether aggregated token-level guidance remains order-consistent with the outcome reward. To this end, we develop an outcome-guided margin calibration mechanism to restore order consistency between correct and incorrect trajectories. We conduct extensive experiments on 5 domains and 16 benchmarks covering diverse settings, including single-teacher and multi-teacher distillation across LLMs and MLLMs, strong-to-weak distillation, and cross-modal distillation. Our results verify the effectiveness and versatility of Uni-OPD and provide practical insights into reliable OPD.

On-Policy Distillation (OPD) improves the learning efficiency of standard reinforcement learning through dense, token-level supervision from teachers. In the standard KL objective of OPD, token-level losses are uniformly averaged, implying equal weights for all tokens. However, we discover that not all tokens are created equal: as student rollouts grow longer, they deviate further from the teacher's distribution, leading to degraded supervision quality at later positions. As a result, OPD using only the first 30% of tokens can perform comparably to using all tokens, whereas OPD using only the last 30% of tokens barely learns anything. In this work, we provide a principled understanding of this issue through the lens of constrained optimization. Based on these insights, we derive Importance-Weighted On-Policy Distillation (IW-OPD), in which the weight assigned to each token depends on the accumulated discrepancy between the student's and teacher's distributions, naturally upweighting earlier tokens and downweighting later ones with larger deviations. We show that IW-OPD converges significantly faster than OPD, with better learning efficiency, and achieves better final performance than standard OPD in both same-size and cross-scale settings, improving performance up to 6.9 points on AIME-2025.

On-policy distillation (OPD) supervises the student only in output space by matching next-token probabilities. This output-only paradigm has two limits: (1) sampling variance from Monte Carlo KL estimates over large vocabularies (e.g., Qwen's ~150k tokens) persists throughout training, and (2) it treats the teacher as a black-box, discarding all intermediate hidden states after the LM head. We propose On-Policy Representation Distillation (OPRD), which lifts distillation into hidden-state space by aligning student and teacher representations across selected layers on the same rollouts, bypassing the LM head entirely. Theoretically, OPRD eliminates sampling variance and provides richer per-layer structural information. Empirically, OPRD closes the student-teacher gap on AIME 2024/2025 and AIMO, while output-space OPD baselines plateau below the teacher. OPRD also trains 1.44x faster and uses 54% less memory than top-k OPD. Code: https://github.com/ShenzhiYang2000/OPRD.

On-Policy Distillation (OPD) has become a core technique in the post-training of Large Language Models (LLMs) for transferring knowledge from domain experts to student models. However, existing OPD distillation methods require teacher and student models to share the same tokenizer, restricting the applicability of OPD within the model series. Current mainstream practice typically employs Supervised Fine-Tuning (SFT) on teacher-generated responses for cross-tokenizer distillation, which fails to capture the rich knowledge embedded in the teacher's probability distribution. In this work, we enable the standard on-policy distillation method to operate across model families, ensuring that high-fidelity token-level signals can propagate across different tokenizers with a precise token-mapping algorithm. Extensive experiments show that cross-tokenizer OPD is significantly more compute-efficient than baselines on various benchmarks. Our results unlock a broader range of teacher-student pairs for OPD, opening up new avenues for adapting and enhancing interactions between LLMs.

Reinforcement learning (RL) has been widely used to train LLM agents for multi-turn interactive tasks, but its sample efficiency is severely limited by sparse rewards and long horizons. On-policy self-distillation (OPSD) alleviates this by providing dense token-level supervision from a privileged teacher that has access to ground-truth answers. However, such fixed privileged information cannot capture the diverse valid strategies in agent tasks, and naively combining OPSD with RL often leads to training collapse. To address these limitations, we introduce Skill-SD, a framework that turns the agent's own trajectories into dynamic training-only supervision. Completed trajectories are summarized into compact natural language skills that describe successful behaviors, mistakes, and workflows. These skills serve as dynamic privileged information conditioning only the teacher, while the student always acts under the plain task prompt and learns to internalize the guidance through distillation. To stabilize the training, we derive an importance-weighted reverse-KL loss to provide gradient-correct token-level distillation, and dynamically synchronize the teacher with the improving student. Experimental results on agentic benchmarks demonstrate that Skill-SD substantially outperforms the standard RL baseline, improving both vanilla GRPO (+14.0%/+10.9% on AppWorld/Sokoban) and vanilla OPD (+42.1%/+40.6%). Project page: https://k1xe.github.io/skill-sd/

We study on-policy distillation (OPD) for agentic tasks, where an LLM agent interacts with an environment over multiple turns and a student imitates a teacher over these multi-turn interaction histories. Fully online OPD is costly because each update requires fresh student rollouts through the environment and teacher queries at visited histories. We propose Replayed-Prefix On-Policy Distillation (ReOPD), an off-environment alternative that reuses pre-collected teacher trajectories as replayed prefixes: the student acts at selected steps, while the teacher provides dense per-step supervision without executing new environment interactions. We show that multi-turn OPD introduces a prefix trap: making histories more student-on-policy improves relevance to the student, but can query the teacher on histories where its target is unreliable. This creates a two-sided distribution shift between student occupancy and teacher reliability. ReOPD addresses this by treating multi-turn OPD as a reliability-aware prefix distribution design and implements it with a simple step-decaying sampling schedule that emphasizes early, lower-shift prefixes. Across mathematical reasoning with Python and search environments over multiple teacher and student model scales, ReOPD preserves or improves OPD-level accuracy, uses zero tool calls during student training, and is at least 4times faster per rollout than OPD. ReOPD therefore turns expensive agent-environment interaction into a reusable offline resource, enabling scalable distillation across tools, tasks, and environments.

On-policy distillation (OPD) has become increasingly popular for transferring teacher capabilities to student models. In this work, we ask a critical research question: Is on-policy sampling always beneficial for distilling arbitrary teacher-student pairs? We show that a simple alternative, Semi-OPD, which distills from offline rollouts generated by the initial student, can often outperform OPD in both accuracy and training efficiency. Across 17 teacher-student pairs ranging from 1.5B to 235B parameters, Semi-OPD outperforms OPD in 14 cases, with up to +13.6% accuracy and 11.4x training speedup. We further find that the choice between OPD and Semi-OPD depends on the alignment between the initial teacher and student, quantified by an output-token overlap ratio: OPD is beneficial only when the two are highly aligned with high overlap ratios. Our deeper investigation suggests that effective distillation requires on-policyness w.r.t. both the student and the teacher. For misaligned pairs, student rollouts can become increasingly off-policy w.r.t. the teacher as context length grows, weakening the distillation signal. In contrast, Semi-OPD is often more stable, as it distills on shorter contexts while covering full trajectories and exposing the student to more teacher-preferred tokens. Beyond proposing Semi-OPD as an efficient alternative, our work motivates the community to rethink when to use OPD and to study stronger OPD variants with meaningful teacher-student pairs.

Diffusion large language models (dLLMs) generate text by iteratively denoising a masked sequence, offering a parallel alternative to autoregressive models, but eliciting strong reasoning through post-training remains difficult: supervised fine-tuning is off-policy and suffers from exposure bias, while reinforcement learning gives only sparse, sequence-level rewards and is hard to apply without tractable sequence likelihoods. On-policy self-distillation (OPSD) offers a promising alternative, using one model as both student and teacher to provide dense, token-level, on-policy supervision, but its effectiveness hinges on giving the teacher privileged information (PI) - typically an instance-specific ground-truth reference unavailable at inference - so the student ends up distilling a weak PI-free consensus policy that yields little improvement on dLLM reasoning. We introduce dOPSD, which instead derives the teacher's privilege directly from the student's own denoising trajectory, evaluating masked positions using later, more-decoded steps of that same trajectory rather than an external label, so the teacher's advantage emerges from the model's own decoding process; on Dream and LLaDA, dOPSD improves both in-domain math reasoning and out-of-domain code generation, outperforming supervised and on-policy baselines.

Training small language-model agents for long-horizon interactive tasks requires both fast imitation and reward-driven improvement. On-policy distillation (OPD) provides dense teacher guidance and typically improves rapidly in the early stage, but its gains saturate once the student approaches the teacher, limiting the final performance ceiling. Reinforcement learning (RL) directly optimizes environment rewards and encourages exploratory improvement toward a higher reward-defined ceiling, but sparse and delayed feedback makes early-stage learning much less efficient than OPD. In this paper, we propose ATOD (Annealed Turn-aware On-policy Distillation), a hybrid online distillation algorithm that explicitly exploits this complementarity. (1) ATOD uses an annealed OPD-RL schedule: OPD dominates early training to approach teacher-level behavior, while RL is gradually strengthened to drive reward-based exploration. (2) ATOD introduces Turn-level Disagreement-Uncertainty Reweighting (T-DUR), which softly amplifies high-utility turns and improves dense supervision in long trajectories. Experiments on ALFWorld, WebShop, and Search-QA show that ATOD consistently outperforms competing post-training baselines: across the three student sizes, ATOD improves average success rate by 3.03 points over OPD and 23.62 points over GRPO, while surpassing the corresponding teacher models by 2.16 points.

On-policy (self) distillation (OPSD) is increasingly adopted for language-model post-training. It strengthens the teacher with privileged information but can induce a privilege illusion: the student learns privilege-dependent behavior it cannot reproduce from its inference-time context, yet behaves as if the training-time privileged information remained available, ultimately degrading performance. In this paper, we identify information asymmetry between the privileged teacher and the student at inference as the root cause of this failure in OPSD. To resolve this asymmetry, we propose Dual-Anchored Policy Distillation (DAPD), a unified framework with two levels of anchoring. Dual-Path Anchoring (DPA) introduces a self-conditioned bridge and aligns reference and rollout behavior along two matched-information paths, preventing privilege-dependent behavior from being transferred to the inference-time student. Dual-Source Anchoring (DSA) applies these paths in both reference-to-rollout and rollout-to-reference directions, reducing reliance on privileged reference guidance while preserving correctness supervision. Extensive experiments show that DAPD significantly alleviates privilege illusion, outperforming OPSD on Qwen3-4B by +2.00 points on average across tasks. Notably, its gains persist across scales, reaching +2.69 at 4B and +2.78 at 32B.

On-policy distillation (OPD) provides dense, per-token supervision for language model post-training, but its effectiveness is bottlenecked by teacher quality: external teachers suffer from distribution mismatch, while self-distillation with privileged conditioning is limited by in-context learning capacity. We propose RISE (Recursive Improvement via Self-Extrapolating Policy Distillation), which constructs a synthetic teacher directly from the model's own RLVR training trajectory. By extrapolating the displacement between the current checkpoint and a trailing anchor---in parameter space or output logit space---RISE converts a sparse outcome-induced parameter update into a dense token-level target, without any external model or privileged conditioning. RISE combines RLVR and OPD in a complementary loop: outcome rewards ground the extrapolation toward correct reasoning, while the extrapolated teacher refines token-level decisions. Moreover, since the teacher is refreshed every iteration as the student improves, distillation becomes a recursive improvement mechanism rather than a one-shot compression step. Experiments spanning mathematical reasoning, multi-domain STEM, code generation, and multi-turn agentic tasks show that RISE outperforms RLVR-only training and on-policy self-distillation across all settings.

On-policy distillation (OPD) is a promising approach for training language agents, providing dense teacher supervision on student-generated trajectories. However, in multi-turn interaction, an incorrect action changes the states the student encounters later, so errors compound across turns. In preliminary experiments across three Qwen3 models (8B to 235B), we find that more than half of the failed rollouts contain a pivotal mistake, an action that moves the agent farther from completing the task, and this mistake typically occurs early. These pivotal mistakes often remain recoverable: guiding the model for only a few turns after the pivotal turn can restore task success. We therefore propose PivotOPD, an on-policy distillation framework that jointly trains the student to prevent pivotal mistakes and to recover from the states they create. At each pivotal mistake, a teacher model provides a gold action and then names a recovery action at each of the next few turns. Preventive distillation uses the gold action with reverse KL to steer the student away from the pivotal mistake, while recovery distillation uses the recovery actions with forward KL to transfer recovery behaviors that the student rarely samples. Against 13 baselines on ALFWorld, WebShop, and Search-based QA, PivotOPD achieves the strongest average performance for both Qwen3-1.7B and Qwen3-8B students, improving over the strongest baseline on ALFWorld by +5.5% with the 1.7B student. The gains also transfer to another model family on the software engineering domain, where PivotOPD raises the resolve rate of a Nemotron-3.5 student on SWE-Bench Verified by +3.2%. Project page: https://research.nvidia.com/labs/lpr/pivotopd/

Standard knowledge distillation for autoregressive models often suffers from distribution mismatch. While on-policy methods mitigate this by leveraging student-generated outputs, they rely on computationally expensive Reinforcement Learning (RL) frameworks. To improve efficiency, we propose Near-Policy Distillation (NPD), an asynchronous approach that decouples student generation from training. This reformulation enables Supervised Fine-Tuning (SFT) with sequence packing. However, asynchronous updates inevitably introduce policy lag and sample noise, which can cause the behavior to drift from near-policy toward off-policy. To counteract this without sacrificing efficiency, NPD integrates sparse student updates and the Δ-IFD filtering mechanism, a heuristic sample selection mechanism that empirically stabilizes the optimization trajectory. By filtering extreme out-of-distribution samples, Δ-IFD prevents noise from dominating the gradients, ensuring updates remain within a safe proximal learning zone. Empirically, the NPD framework achieves a 8.1x speedup over on-policy baselines and outperforms SFT by 8.09%. Crucially, by effectively narrowing the exploration space for subsequent RL, our method enables openPangu-Embedded-1B to reach a state-of-the-art score of 68.73%, outperforming the substantially larger Qwen3-1.7B. Codes will be released soon.

On-policy distillation (OPD) trains student models under their own induced distribution while leveraging supervision from stronger teachers. We identify a failure mode of OPD: as training progresses, on-policy rollouts can undergo abrupt length inflation, causing truncated trajectories to dominate the training data. This truncation collapse coincides with abrupt repetition saturation and induces biased gradient signals, leading to severe training instability and sharp degradation in validation performance. We attribute this problem to the interaction between student-induced data collection and the distillation objective, which implicitly favors long and repetitive rollouts. To address this issue, we propose StableOPD, a stabilized OPD framework that combines a reference-based divergence constraint with rollout mixture distillation. These together mitigate repetition-induced length inflation and further stabilize OPD training. Across multiple math reasoning datasets, our approach prevents truncation collapse, stabilizes training dynamics, and improves performance by 7.2% on average.

On-policy distillation (OPD) trains a student on its own rollouts using dense supervision from a teacher. In multi-turn environments, a mistake at a critical decision step can redirect the subsequent rollout toward poor outcomes. We use low teacher confidence on student actions to select high-uncertainty steps for correction. In a controlled ALFWorld study, a single teacher correction at a low-confidence step improves subsequent student behavior and task success, motivating selective intervention during distillation. We propose UOPD, an uncertainty-aware intervention method for on-policy distillation. At low-uncertainty turns, UOPD executes student actions and applies the standard OPD loss. At high-uncertainty turns, it samples and executes teacher actions and trains the student to imitate them through supervised fine-tuning, which minimizes forward Kullback-Leibler divergence in expectation. UOPD utilizes adaptive uncertainty thresholds to target a scheduled intervention rate. Empirically, we evaluate UOPD across a broad range of agentic tasks, including ALFWorld, WebShop, and Search, demonstrating its superior performance over OPD methods and their variants. UOPD improves WebShop score by up to 15.8% relative to standard OPD.

On-policy distillation (OPD) transfers teacher knowledge to a student through feedback on student-generated rollouts, but generating complete rollouts and computing per-token teacher feedback are computationally expensive. Existing truncation methods save computation by stopping rollouts early. However, they do not compensate for truncated token gradients, which biases the gradient estimates and changes Vanilla OPD's original training objective. Furthermore, their truncation decisions rely on assumptions about supervision quality or criteria that may not generalize across settings. We introduce Stochastic Truncated On-Policy Distillation (STOPD), which accelerates OPD by randomly truncating student rollouts and correcting the resulting sampling bias with blockwise inverse-probability weighting (IPW). At each training step, we sample a stopping position for each rollout before generation and let the student generate until that position or natural termination. We obtain teacher feedback on every generated token and use blockwise IPW to compensate for the lower probability of retaining later tokens while controlling the weights. We prove that this weighting preserves Vanilla OPD's gradient sum in expectation and derive one-step update-error bounds for SGD, Adam, and Muon. We evaluate STOPD across multiple teacher-student model pairs, task domains, and optimizers. STOPD reduces generated tokens by 25-48% while maintaining accuracy comparable to Vanilla OPD, achieving 1.3-2.2x training speedups.

On-policy distillation has recently emerged as a promising alternative to standard sequence-level imitation, training a student by scoring its own rollouts with a teacher model. However, we observe ``Off-policy Teacher Decay'' problem in this paradigm: for the later tokens, with student's earlier trajectory as context that is off-policy to the teacher, the teacher's ability to produce a corrective score would decay, and may fall back to token-completion behavior learned in the pre-training stage. We empirically verify this problem, and we propose Early Stopping Rollout (ESR) to fix it: a simple yet effective distillation strategy that simply restricts the rollout generation to the first response tokens. We show that ESR both surpasses the full rollout OPD performance across model size, family, tasks and training regime, and exhibit much higher GPU efficiency and training stability, especially under cross model family scenarios. We further investigate the mechanism behind this surprising performance and discovered "Cascading Alignment" and "Sub-mode Commitment" effect of ESR that may explain why it works effectively and even sometimes exceeding the teacher model performance. Besides, we show that this position-based token selection strategy cannot be fully explainable by KL divergence and entropy signals.

On-policy self-distillation (OPSD) combines student generated trajectories with dense supervision from a privileged teacher of the same model. Its pointwise clipping protects the student from locally incompatible teacher directions, but the fixed teacher receives no feedback about the supervision the student rejects, which limits effective learning from the teacher. We introduce DualOPSD, which alternates updates in a coupled teacher-student system. The student retains OPSD's clipped forward KL objective. The privileged teacher adapts to the updated student after each student step. A residual target based on the frozen initial model preserves the effect of privileged context during teacher adaptation. Across Qwen3-8B/4B/1.7B and three math benchmarks, DualOPSD improves avg@12 accuracy over OPSD by 9.83 percentage points. Further diagnostic analyses show lower bidirectional KL, less persistent mismatch, and retained sensitivity to privileged reference. Together, these results demonstrate that DualOPSD can be a more effective form of privileged self-distillation. Code is available at: https://github.com/on1262/DualOPSD.

On-policy distillation (OPD) offers superior capacity transfer by supervising student-sampled trajectories with dense token-level signals. To furnish high-quality supervision sources and thereby elevate the performance frontier of distillation, an intuitive direction is to infuse privileged information to either teacher or student itself. However, this additional input induces a potential failure mode we dub privilege illusion: a pattern that conflates the transferable capability gap that students are meant to close, and the information asymmetry gap that can only be mimicked but never replicated. This issue is further amplified by the inherent non-uniformity of token-level supervision, where only a small subset of tokens carries pivotal capability-bearing signals. To this end, we propose DOPD, an advantage-aware dual distillation paradigm that dynamically routes token-level supervision between privileged teacher and privileged student policies based on their advantage gap and relative probabilities. Each token receives supervision of different strength, objective, and strategy from either teacher or student itself, which transfers credible capability while simultaneously receiving auxiliary signals, to alleviate privilege illusion. Extensive experiments on both large language model (LLM) and vision-language model (VLM) settings demonstrate that DOPD consistently outperforms Vanilla OPD and other counterparts. Further results on stability, robustness, continual learning, and out-of-distribution tasks validate its superiority.

On-policy distillation (OPD) has recently emerged as an important post-training paradigm. By using a stronger teacher model to provide dense, fine-grained supervision for sampled trajectories, OPD offers a clear advantage over reinforcement learning with verifiable rewards (RLVR), which typically depends on sparse binary or outcome-based environmental feedback. However, naive token-level distillation can suffer from gradient instability, due to magnitude misalignment in outlier states. To address this issue, we propose Globally Normalized Distillation Policy Optimization (GNDPO), a practical method that stabilizes optimization by transforming raw KL scores into batch-level relative advantages. This normalization effectively mitigates gradient explosions while retaining the benefits of token-level guidance. Experimental results show that GNDPO substantially improves training robustness and downstream performance across multimodal reasoning tasks. The code is released at https://github.com/OPPO-Mente-Lab/GNDPO.

On-Policy Distillation (OPD) is emerging as a promising alternative to reinforcement learning for LLM post-training, yet its effectiveness in multilingual settings remains underexplored. We study OPD and its advanced variant, On-Policy Delta Distillation (OPD^2), for mathematical reasoning in English, Korean, and Japanese. OPD^2 improves OPD by using the probability gap between a post-trained teacher and its base model as the learning signal. Experiments with Qwen3 show that OPD^2 consistently outperforms the original OPD, with particularly strong improvements in Korean and Japanese, and generally narrows the English-Korean performance gap. We further find that English-only OPD can also increase performance for Korean and Japanese, but often shifts the responses toward English, highlighting the importance of multilingual data to preserving target-language responses.

On-policy distillation (OPD) trains agents on their own trajectories using supervision from a stronger teacher. We uncover a counterintuitive phenomenon in multi-turn agentic tasks: a smaller, initially weaker student can substantially outperform its teacher during training, only to regress as distillation continues. We term this phenomenon distillation overshoot. Through decision- and task-level analyses, we trace overshoot to two competing effects of OPD: repairing weak student decisions and eroding successful student choices that the teacher disfavors. Early in training, repair outpaces erosion, allowing the student to combine the teacher's corrections with its own strengths and surpass the teacher. As training continues, erosion overtakes repair, causing these gains to vanish. Motivated by this finding, we propose Success-Preserving On-Policy Distillation (SPOD), which selectively masks conflicting teacher supervision on successful student choices and introduces a soft probability floor to counteract their erosion, while retaining teacher guidance elsewhere. SPOD requires only binary episode success and model probabilities already available during OPD. Across two model families and three agentic benchmarks, SPOD consistently outperforms ordinary OPD and evaluated variants, improving final success by up to 15.2 percentage points and surpassing the teacher by up to 20.0 points. Moreover, SPOD's final checkpoints outperform even ordinary OPD's best intermediate checkpoints in all six settings, demonstrating that beyond-teacher gains can be not only preserved but further extended. Code: https://github.com/Jike338/SPOD

Compact instruction-following rerankers are attractive for deployment, but conventional distillation pipelines typically train students by offline imitation of teacher outputs on a fixed set of examples, constraining supervision to the teacher's observed ranking space. We revisit reranker distillation through the lens of reinforcement learning. We propose a two-stage framework combining off-policy teacher optimization with on-policy student distillation. In Stage 1, a 4B teacher reranker is strengthened with off-policy GRPO using LLM-judge feedback on 88K instruction-following examples. In Stage 2, a compact 1B student samples rankings from its own policy and receives soft teacher-derived rewards on those rankings, coupling student exploration with knowledge transfer. Our strongest gains appear under distribution shift. On MAIR-11, the original 11-subset, 869-query evaluation, the proposed student reaches 0.7670 nDCG@6, outperforming offline listwise KD by +4.6 points. Controlled comparisons against offline pairwise RankNet KD and on-policy GKD show that neither changing the offline distillation objective nor moving teacher-distribution matching on-policy reproduces the performance of reward-based on-policy distillation over student-sampled rankings. The advantage persists on MAIR-Full: across all 126 tasks and 9,356 queries, the proposed method obtains the highest task-macro point estimates among the evaluated distillation variants, reaching 0.6808 nDCG@6 and 0.7865 MRR@6. It also exceeds two released 7B RL-trained rerankers on the comparable MAIR-11 evaluation, while the same Stage 2 training procedure consistently improves three architecturally distinct alternative student backbones. On the 9,861-query validation benchmark, the resulting 1B reranker achieves 0.7624 nDCG@6 while providing a favorable quality-efficiency tradeoff relative to larger alternatives.

Knowledge distillation offers a promising path to transfer reasoning capabilities from large teacher models to efficient student models; however, existing token-level on-policy distillation methods require token-level alignment between the student and teacher models, which restricts the student model's exploration ability, prevent effective use of interactive environment feedback, and suffer from severe memory bottlenecks in reinforcement learning. We introduce On-policy Verbal Distillation (OVD), a memory-efficient framework that replaces token-level probability matching with trajectory matching using discrete verbal scores (0--9) from teacher models. OVD dramatically reduces memory consumption while enabling on-policy distillation from teacher models with verbal feedback, and avoids token-level alignment, allowing the student model to freely explore the output space. Extensive experiments on Web question answering and mathematical reasoning tasks show that OVD substantially outperforms existing methods, delivering up to +12.9% absolute improvement in average EM on Web Q&A tasks and a up to +25.7% gain on math benchmarks (when trained with only one random samples), while also exhibiting superior training efficiency. Our project page is available at https://OVD.github.io

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models (LLMs). While Group Relative Policy Optimization (GRPO) is widely adopted, it suffers from sparse reward signals and loses gradients entirely when all responses within a group receive identical rewards. On-policy distillation (OPD) offers a natural remedy by providing dense, token-level supervision from a teacher model. However, naively combining GRPO with OPD leads to degraded performance, due to three underlying causes: not all samples benefit from distillation; fitting too quickly to the teacher undermines the exploratory capacity of RL; and OPD's advantages are asymmetric, suppressing most tokens. To address these challenges, we propose RSTG (Recovering Learning Signals via Adaptive Teacher Guidance), which applies distillation selectively and precisely where it matters most. At the sample level, OPD is restricted to negative zero-variance prompts with each sample weighted by the teacher's confidence score. At the token level, distillation targets only tokens with high student entropy or large teacher-student divergence. We further augment training with SFT on correct trajectories generated by the teacher model, injecting positive gradient signals where RL yields none. Experiments demonstrate that RSTG substantially outperforms naive GRPO+OPD by +4.02% on math and +3.05% on code.

On-policy distillation (OPD) trains a student model on its own rollouts with token-level supervision from a teacher, assuming that the teacher can reach a correct answer from any prefix the student writes. We call this property the recoverability of the teacher and show it fails on incorrect rollouts: the teacher follows student errors, although it recognizes them. We propose CriticOPD, using error recognition to restore recoverability. The teacher critiques an incorrect rollout, allowing the student to rewrite its solution following the error. The resulting output, including the critique as privileged information, is scored by the teacher while the student uses the revision without the critique for training. On two Qwen3 students and six mathematical reasoning benchmarks, CriticOPD improves OPD, with the largest gains on competition problems.

On-policy distillation (OPD) has become a popular training paradigm in the LLM community. This paradigm selects a larger model as the teacher to provide dense, fine-grained signals for each sampled trajectory, in contrast to reinforcement learning with verifiable rewards (RLVR), which only obtains sparse signals from verifiable outcomes in the environment. Recently, the community has explored on-policy self-distillation (OPSD), where the same model serves as both teacher and student, with the teacher receiving additional privileged information such as reference answers to enable self-evolution. This paper demonstrates that learning signals solely derived from the privileged teacher result in severe information leakage and unstable long-term training. Accordingly, we identify the optimal niche for self-distillation and propose RLSD (RLVR with Self-Distillation). Specifically, we leverage self-distillation to obtain token-level policy differences for determining fine-grained update magnitudes, while continuing to use RLVR to derive reliable update directions from environmental feedback (e.g., response correctness). This enables RLSD to simultaneously harness the strengths of both RLVR and OPSD, achieving a higher convergence ceiling and superior training stability.

Reinforcement Learning (RL) from outcome rewards suffers from sparse supervision, particularly on difficult, long-horizon tasks where successful trajectories are rare and costly to generate. On-Policy Distillation (OPD) offers an attractive alternative by providing dense token-level supervision from a stronger teacher along the student's own generations. Self-distillation methods further remove the need for a separate teacher model by conditioning the same policy on privileged information to serve as its own teacher. However, privileged conditioning alone does not guarantee that the resulting distillation update improves the student. Indeed, privileged information can lead the teacher to solve tasks through shortcuts unavailable to the student, producing supervision poorly matched to the student's current behavior. Consequently, even a higher-performing teacher can provide guidance that degrades student performance. To address this, we analyze how the choice of privileged teacher affects the student's update. We derive a necessary and sufficient condition for the teacher's local distillation update to be a positive multiple of the student's reward gradient. Our analysis suggests that the teacher should not only perform well on the task, but also provide guidance suited to the student's current capabilities. This characterization motivates a practical teacher-training surrogate that combines outcome rewards with token-level Kullback-Leibler (KL) regularization toward the student. Based on this result, we propose Joint On-Policy Learning and Teaching (JOLT), which jointly trains a single policy in two roles: a privileged teacher using a KL-regularized objective, and an unprivileged student using dense on-policy distillation. Across mathematical reasoning, coding, tool use, and terminal use, JOLT improves training efficiency and performance, with further gains from student rewards.

Diffusion distillation models effectively accelerate reverse sampling by compressing the process into fewer steps. However, these models still exhibit a performance gap compared to their pre-trained diffusion model counterparts, exacerbated by distribution shifts and accumulated errors during multi-step sampling. To address this, we introduce Distillation++, a novel inference-time distillation framework that reduces this gap by incorporating teacher-guided refinement during sampling. Inspired by recent advances in conditional sampling, our approach recasts student model sampling as a proximal optimization problem with a score distillation sampling loss (SDS). To this end, we integrate distillation optimization during reverse sampling, which can be viewed as teacher guidance that drives student sampling trajectory towards the clean manifold using pre-trained diffusion models. Thus, Distillation++ improves the denoising process in real-time without additional source data or fine-tuning. Distillation++ demonstrates substantial improvements over state-of-the-art distillation baselines, particularly in early sampling stages, positioning itself as a robust guided sampling process crafted for diffusion distillation models. Code: https://github.com/geonyeong-park/inference_distillation.

On-policy self-distillation (OPSD) is an emerging LLM post-training paradigm in which the model serves as its own teacher: conditioned on privileged information such as a reference trace or hint, the same policy provides dense token-level supervision on its own rollouts. However, recent studies show that OPSD degrades complex reasoning by suppressing predictive uncertainty, which supports exploration and hypothesis revision. Our token-level analysis shows that this failure arises from applying a uniform direction of teacher supervision across tokens with different uncertainty levels: conformity to the privileged self-teacher suppresses exploration at high entropy, while deviation from the teacher degrades step accuracy at low entropy. Accordingly, we propose Direction-Adaptive Self-Distillation (DASD), which reframes privileged self-distillation from uniform teacher imitation into entropy-routed directional supervision: high-entropy tokens are pushed away from the privileged teacher to preserve exploration, while low-entropy tokens are pulled toward the teacher to stabilize step-level execution. Across six mathematical reasoning benchmarks, DASD achieves the best macro Avg@16 over strong RLVR and self-distillation baselines. Pass@k, reasoning-health, and generalization analyses show that these average gains come from preserving exploration without sacrificing step-level execution.

On-policy reinforcement learning has become the dominant paradigm for reasoning alignment in large language models, yet its sparse, outcome-level rewards make token-level credit assignment notoriously difficult. On-Policy Distillation (OPD) alleviates this by introducing dense, token-level KL supervision from a teacher model, but typically applies this supervision uniformly across all rollouts, ignoring fundamental differences in signal quality. We propose Signal-Calibrated On-Policy Distillation Enhancement (SCOPE), a dual-path adaptive training framework that routes on-policy rollouts by correctness into two complementary supervision paths. For incorrect trajectories, SCOPE performs teacher-perplexity-weighted KL distillation to prioritize instances where the teacher demonstrates genuine corrective capability, while down-weighting unreliable guidance. For correct trajectories, it applies student-perplexity-weighted MLE to concentrate reinforcement on low-confidence samples at the capability boundary rather than over-reinforcing already mastered ones. Both paths employ a group-level normalization to adaptively calibrate weight distributions, accounting for the intrinsic difficulty variance across prompts. Extensive experiments on six reasoning benchmarks show that SCOPE achieves an average relative improvement of 11.42% in Avg@32 and 7.30% in Pass@32 over competitive baselines, demonstrating its consistent effectiveness.

Text-Image-to-Video (TI2V) models are an emerging unified architecture, where a single model simultaneously supports text-to-video (T2V) and image-to-video (I2V) generation. Given a high-quality first frame or a detailed textual prompt, TI2V models unlock substantially better visual quality than their T2V mode, raising a natural question: can the capability elicited by such privileged conditions be internalized into the model's own base generation ability? A common approach toward this goal is model self-distillation. However, the most straightforward solution, supervised fine-tuning, follows an off-policy strategy: its supervision is confined to teacher-generated endpoints from a fixed offline distribution rather than student-visited states, lacking precise correction tailored to the evolving policy. Recent on-policy distillation methods instead suffer from condition-state mismatch, where supervision is steered toward the given first frame instead of the student's actual content, misleading the correction. To achieve self-distillation that absorbs the teacher's privileged prior while retaining precise policy correction, in this work, we propose Hybrid-Policy Self-Distillation (HPSD), a novel self-distillation framework where a single TI2V model acts as both teacher and student under different conditions: the teacher operates in TI2V mode with a high-quality first frame and an enhanced prompt, while the student runs in the base T2V mode with only the vanilla prompt. Specifically, the student inherits off-policy teacher trajectory points as anchors, locally refines them toward its own policy, and finally receives velocity-level supervision on these self-generated roll-outs. Extensive experiments demonstrate that HPSD significantly improves T2V performance while also delivering notable TI2V gains, effectively strengthening the model's base generation ability.

On-policy distillation (OPD) has recently emerged as a promising post-training paradigm in which the student learns from trajectories generated by its own policy under dense teacher supervision. However, OPD introduces a fundamental asymmetry: although the sampled trajectories are on-policy for the student, they are off-policy for the teacher. The teacher is typically optimized to continue from prefixes generated by its own policy, but during OPD it must instead supervise prefixes generated by the student. Empirically, we find that its continuation performance degrades as these prefixes grow longer. To address this issue, we propose Student-COnditioned Updates of the Teacher (SCOUT), a co-training framework that adapts the teacher to student-generated prefixes. Alongside standard OPD updates, SCOUT periodically optimizes the teacher's conditional ability using reinforcement learning with verifiable rewards, where the teacher generates continuations from student prefixes and learns from outcome rewards. Controlled experiments show that SCOUT improves the teacher's ability to continue from student-generated prefixes, supporting the intended mechanism of student-conditioned teacher adaptation. Across multiple teacher--student configurations, model scales, and reasoning domains, SCOUT also consistently improves the effectiveness of on-policy distillation.

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models on tasks such as mathematical reasoning and code generation. However, most RLVR methods assign a scalar outcome reward to an entire trajectory, resulting in sparse supervision and limited token-level credit assignment. On-policy distillation (OPD) provides denser supervision by distilling token-level distributions from a stronger teacher model, but requires an additional teacher and typically assumes a shared vocabulary. On-policy self-distillation (OPSD) removes this dependency by conditioning the same model on privileged information to construct a teacher policy. However, directly matching the teacher distribution may cause information leakage and unstable optimization. RLSD avoids direct matching by using the teacher signal only to modulate update magnitudes, but it cannot provide an explicit correction direction when the sampled reasoning fails. To address this tradeoff, we introduce H^{2}SD, a hybrid hindsight self distillation framework that uses the teacher differently according to trajectory correctness. For successful trajectories, the teacher receives the student response confirmed as correct together with a rephrasing instruction, and its probabilities on the original response tokens are used to modulate update magnitudes without changing the direction determined by the reward. For failed trajectories, we condition the teacher on a reference hint containing key reasoning steps and a verified answer, and minimize the reverse KL divergence from the student to the teacher. Experiments on multiple challenging reasoning benchmarks show that H^2SD consistently outperforms representative RLVR, OPSD, and RLSD baselines while maintaining stable optimization and favorable generation efficiency.

Long-horizon agentic RL is constrained by the futures visited by the current policy. When rollouts fail to reach useful behaviors, improved credit assignment cannot provide supervision for states and actions that were never encountered. On-policy distillation (OPD) introduces teacher guidance on policy-induced states, and recent multi-turn variants improve how this guidance is scheduled, replayed, refined, or validated. However, they do not directly use the oracle-controlled future itself as the training trajectory. We introduce State-Rooted Executable Rollout Optimization (SERO), which augments on-policy agentic RL with executable oracle continuations. SERO restores a state actually reached by the current policy and lets a training-only oracle continue interacting with the real environment, making the downstream observations and oracle actions themselves available for learning. It then applies policy-reachability weighting, which weights each oracle step by the frozen behavior policy's compatibility with the preceding oracle actions. This allows deeper supervision to become effective as the policy becomes more compatible with the oracle branch. The oracle loss is optimized separately from the base RL estimator and no oracle is used at inference time. We evaluate SERO on two challenging interactive-agent benchmarks, ALFWorld and WebShop, using Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct. On ALFWorld, learning the full executable continuation is substantially more effective than supervising only the root oracle action, while policy-reachability weighting further improves out-of-distribution performance.

On-policy self-distillation, where a language model conditions on privileged context to supervise its own generations, is a promising source of dense supervision for sparse-reward reinforcement learning. Actually, it can be instantiated as an auxiliary full-vocabulary student-to-teacher reverse Kullback-Leibler divergence loss. We therefore propose SDPG, a self-distilled policy-gradient framework that combines group-relative verifier advantages with normalized standard deviation, exact full-vocabulary on-policy self-distillation, as well as reference-policy KL regularization. Empirically, SDPG improves stability and performance over RLVR and self-distillation baselines. The code is available at https://github.com/lauyikfung/SDPG.

On-policy distillation (OPD) is an increasingly important paradigm for post-training language models. However, we identify a pervasive Scaling Law of Miscalibration: while OPD effectively improves task accuracy, it systematically traps models in severe overconfidence. We trace this failure to an information mismatch: teacher supervision is formed under privileged context available during training, whereas the deployed model must report confidence using only deployment-time information. We formalize this perspective theoretically, showing that teacher-conditioned success is generally not a valid target for deployment-time confidence and that helpful privileged context induces entropy collapse and a systematic optimism bias. To address this, we propose a calibration-aware OPD framework, CaOPD, that estimates empirical confidence from model rollouts, replaces self-reported confidence with this student-grounded target, and distills the revised response through the same self-distillation pipeline. Experiments across various models and domains show that CaOPD achieves Pareto-optimal calibration while maintaining competitive capability, generalizing robustly under out-of-distribution and continual learning. Our findings highlight that capability distillation does not imply calibrated confidence, and that confidence should be treated as an essential objective in post-training. Code: https://github.com/SalesforceAIResearch/CaOPD

On-policy distillation (OPD), which aligns the student with the teacher's logit distribution on student-generated trajectories, has demonstrated strong empirical gains in improving student performance and often outperforms off-policy distillation and reinforcement learning (RL) paradigms. In this work, we first theoretically show that OPD is a special case of dense KL-constrained RL where the reward function and the KL regularization are always weighted equally and the reference model can by any model. Then, we propose the Generalized On-Policy Distillation (G-OPD) framework, which extends the standard OPD objective by introducing a flexible reference model and a reward scaling factor that controls the relative weight of the reward term against the KL regularization. Through comprehensive experiments on math reasoning and code generation tasks, we derive two novel insights: (1) Setting the reward scaling factor to be greater than 1 (i.e., reward extrapolation), which we term ExOPD, consistently improves over standard OPD across a range of teacher-student size pairings. In particular, in the setting where we merge the knowledge from different domain experts, obtained by applying domain-specific RL to the same student model, back into the original student, ExOPD enables the student to even surpass the teacher's performance boundary and outperform the domain teachers. (2) Building on ExOPD, we further find that in the strong-to-weak distillation setting (i.e., distilling a smaller student from a larger teacher), performing reward correction by choosing the reference model as the teacher's base model before RL yields a more accurate reward signal and further improves distillation performance. However, this choice assumes access to the teacher's pre-RL variant and incurs more computational overhead. We hope our work offers new insights for future research on OPD.

On-policy distillation (OPD) has emerged as a widely used paradigm for post-training large language models, reducing the train--test mismatch of conventional distillation by supervising the student on its own generated trajectories. However, existing OPD objectives remain largely token-local and outcome-agnostic, optimizing teacher--student agreement at each prefix despite reasoning quality being determined at the trajectory level. Reinforcement learning with verifiable rewards (RLVR), particularly Group Relative Policy Optimization (GRPO), provides complementary outcome-level supervision but suffers from sparse rewards and coarse credit assignment. We show that OPD and RLVR exhibit complementary blind spots: teacher signals provide dense local guidance but are weakly aligned with rollout correctness, whereas group-relative rewards capture task success but provide coarse token-level credit and vanish on all-failure groups. We introduce DiffGate, an outcome-gated objective that combines GRPO with selective, bounded teacher guidance. Teacher supervision is applied only to failed trajectories, scaled by group difficulty, and smoothly bounded to prevent extreme teacher--student discrepancies from dominating optimization. The verifier therefore determines which trajectories receive teacher guidance, while the teacher provides dense token-level update directions within those trajectories. Across Qwen3-0.6B and Qwen3-1.7B students, DiffGate improves code avg@8 over matched GRPO by +1.7 and +1.8 points and pass@8 by +1.6 and +5.7 points, respectively. On mathematics, avg@8 remains within 0.5 points of GRPO while pass@8 improves by +1.1 and +3.9 points. Overall, DiffGate improves pass@8 across all four model--domain settings, demonstrating improved solution coverage under our evaluation protocol.

Tool-integrated reasoning (TIR) is difficult to scale to small language models due to instability in long-horizon tool interactions and limited model capacity. While reinforcement learning methods like group relative policy optimization provide only sparse outcome-level rewards. Recently, on-policy distillation (OPD) has gained popularity by supplying dense token-level supervision from a teacher on student-generated trajectories. However, our experiments indicate that applying OPD to TIR leads to a critical failure mode: erroneous tool calls tend to cascade across subsequent reasoning steps, progressively amplifying student-teacher divergence and rendering the teacher's token-level supervision increasingly unreliable. To address this, we propose SOD, a step-wise on-policy distillation framework for small language model agents, which adaptively reweights distillation strength at each step based on step-level divergence. Therefore, SOD can attenuate potentially misleading teacher signals in high-divergence regions while preserving dense guidance in well-aligned states. Experiments on challenging math, science, and code benchmarks show that SOD achieves up to 20.86% improvement over the second-best baseline. Notably, our 0.6B student achieves 26.13% on AIME 2025, demonstrating effective transfer of agentic reasoning to lightweight models. Our code is available at https://github.com/YoungZ365/SOD.

Black-box knowledge distillation for large language models presents a strict trade-off. Simple off-policy methods (e.g., sequence-level knowledge distillation) struggle to correct the student's inherent errors. Fully on-policy methods (e.g., Generative Adversarial Distillation) solve this via adversarial training but introduce well-known training instability and crippling computational overhead. To address this dilemma, we propose SODA (Semi On-policy Distillation with Alignment), a highly efficient alternative motivated by the inherent capability gap between frontier teachers and much smaller base models. Because a compact student model's natural, zero-shot responses are almost strictly inferior to the powerful teacher's targets, we can construct a highly effective contrastive signal simply by pairing the teacher's optimal response with a one-time static snapshot of the student's outputs. This demonstrates that exposing the small student to its own static inferior behaviors is sufficient for high-quality distribution alignment, eliminating the need for costly dynamic rollouts and fragile adversarial balancing. Extensive evaluations across four compact Qwen2.5 and Llama-3 models validate this semi on-policy paradigm. SODA matches or outperforms the state-of-the-art methods on 15 out of 16 benchmark results. More importantly, it achieves this superior distillation quality while training 10 times faster, consuming 27% less peak GPU memory, and completely eliminating adversarial instability.

On-policy distillation (OPD) transfers knowledge between language models through teacher supervision on student-generated trajectories. With different tokenizers, a single teacher token may require multiple student tokens to generate, creating intermediate states where the event is entered but not yet completed. Existing cross-tokenizer methods align tokens or text spans to construct comparable prediction targets. We study a complementary problem after partial generation: once the student produces a prefix of a teacher token, multiple next tokens may complete the same remaining bytes, but the teacher only specifies the required completion rather than how probability should be divided among these valid continuations. We introduce Event-Set Completion Distillation (ESCD), which complements cross-tokenizer probability alignment with completion-set supervision. ESCD aggregates prefix-related teacher events and supervises the total probability of byte-compatible one-step student completions, avoiding tokenizer-dependent probability splits among individual tokens. The method reuses student trajectories and predictions, requiring neither additional rollouts nor changes to the student vocabulary. Experiments demonstrate consistent gains in mathematics, code, and scientific reasoning across model families and tokenizers, extending to large-scale MoE distillation from a 1T teacher to a 35B student. Local analyses show that retaining completion sets better matches the reference supervision, while one-step completion covers over 99% of observed compatible teacher mass after partial event entry in the studied tokenizer pairs. These findings support event entry and event completion as complementary supervision targets for cross-tokenizer knowledge transfer. Code will be released on GitHub.

On-policy distillation (OPD) consolidates expert capabilities into a single student by matching teacher and student final-layer distributions on student-generated rollouts. We investigate whether depthwise prediction transitions, the changes in predictions between layers, can provide additional task-relevant supervision. Our diagnostic study finds that stronger teacher--student agreement in intermediate transitions is associated with higher answer correctness within questions, with correct responses exhibiting lower mean transition KL across all measured intermediate layer pairs. These observations motivate On-Policy Transition Distillation (OPTD), which augments final-layer distribution matching by aligning teacher and student layer-to-layer log-probability increments on student-generated rollouts. Evaluations across three backbones and eight benchmarks spanning mathematics, coding, and instruction following show that OPTD achieves the best or tied-best overall performance in both dual- and three-domain distillation. In the three-domain setting, OPTD recovers approx 90% of the overall teacher--student capability gap, compared with approx 75% for OPD.

On-policy distillation (OPD) can succeed with surprisingly few training questions, motivating a view of questions as carriers of distributional knowledge transfer. How can we assess whether a newly generated question is valuable for distillation, and learn to generate better questions---without access to its correct answer? We introduce Ask-to-Distill (\method), a framework that treats synthetic questions as distribution elicitors and optimizes the teacher supervision they expose along student-generated trajectories. A student-initialized synthesizer is optimized using a distributional surrogate for question value, computed from a frozen student--teacher pair without reference answers, correctness rewards, or per-candidate student updates. The reward combines teacher--student disagreement with teacher probability mass on the student's candidate support, together with length and diversity controls. The generated questions are filtered and deduplicated into a prompt-only bank for standard OPD. Across mathematical reasoning, code generation, and agentic tasks, our method improves average performance and teacher-gap recovery over unoptimized student-generated prompts and KL-filtered real questions, while matching or exceeding real-bank OPD in the evaluated settings. Signal analyses further show that optimized questions can elicit denser supervision and more total signal from shorter student responses, supporting elicited distributional supervision as an objective for synthetic distillation data. Our code, data and models are publicly available at https://github.com/GasolSun36/Ask_to_Distill.

On-policy distillation (OPD) trains a student policy by matching a stronger teacher on the student's own trajectories, offering a promising framework for language agent training. However, its application to long-horizon agentic tasks remains insufficiently explored. We identify two key inefficiencies in vanilla agent OPD: (1) full-horizon rollouts often waste wall-clock resources on tail turns that provide weak and noisy KL supervision, and (2) trajectory-level KL objectives concentrate most of the loss on shallow tokens, leaving deeper decision turns under-trained once initial behaviors are aligned. To address these challenges, we propose TurnOPD, a turn-level budgeting strategy for efficient on-policy distillation of long-horizon agents. TurnOPD consists of two budget controllers: adaptive rollout-depth budgeting, which uses probe-based turn statistics to determine rollout length, and progressive turn-normalized loss budgeting, which gradually shifts KL weighting from token-level to turn-balanced supervision. Experiments on ALFWorld, WebShop, and Multi-Hop Search with task-specialized teacher models show that TurnOPD achieves superior validation accuracy under equal wall-clock training budgets and advances the accuracy--time frontier beyond vanilla OPD.

On-policy distillation (OPD) trains a target policy on its own rollouts using token-level supervision from a stronger teacher, but typically relies on the teacher being substantially more capable than the target. Recent work relaxes this requirement by transferring the relative policy difference between an expert and a reference policy rather than the expert's absolute distribution. Yet it remains unclear which differences provide useful supervision and which targets can benefit from them. We develop a unified view in which the log-probability ratio between a proxy expert and a proxy reference defines an implicit reward for KL-regularized policy optimization. This formulation induces an on-policy update for the target, recovers conventional OPD as a special case, and enables any-to-any transfer across models that differ in scale, training stage or generation. Our systematic experiments yield three findings. First, a stronger expert is not necessarily a better source of supervision: differences induced by task-specific training, including reinforcement learning and supervised fine-tuning, transfer consistently, whereas those arising from model scale alone transfer weakly or not at all. Second, the expert and reference serve complementary roles: the expert provides the capability to be transferred, while the reference filters out shared behavior and isolates the relevant residual. Third, even a useful difference does not transfer to every target: success requires the induced update to move the target toward the expert and generalize beyond sampled rollouts. Raw policy distance does not predict transferability, whereas an appropriate reference can rescue otherwise unsuccessful transfer. These results characterize when relative policy differences provide effective supervision for OPD.

On-policy Distillation (OPD) supervises a student model on trajectories sampled from its own policy by minimizing the divergence between the output distributions of the teacher and student at each token position, thereby providing dense token-level supervision. Although existing OPD methods have demonstrated strong performance in improving the reasoning ability of student models, their objectives fundamentally rely on token-level distribution matching. Consequently, they lack an explicit signal for comparing a token's relative compatibility across reasoning modes and thus do not directly model preferences between these modes. To address this limitation, we propose COPD, a contrastive OPD framework. Specifically, for each token generated by the student model, a frozen teacher model scores the same student state under two contrasting instructions that elicit light and heavy reasoning. The difference between the resulting log probabilities serves as a token-level advantage signal to guide the OPD update. Rather than merely imitating a single teacher distribution, COPD directly encourages the student model to learn more concise and efficient reasoning strategies. We conduct experiments on nine multimodal benchmarks covering both reasoning and understanding tasks. The results show that COPD substantially reduces reasoning length without compromising model performance and consistently improves efficiency across different tasks and model scales. Furthermore, the contrastive formulation can be seamlessly integrated into the On-policy Self-distillation (OPSD) framework, where self-contrastive supervision is constructed without an additional teacher model, thereby enabling the model to distill itself toward lightweight reasoning.

On-policy distillation (OPD) combines student-generated rollouts with dense token-level supervision from a teacher. Existing work has mainly studied its algorithmic behavior, leaving the role of training data unclear. We examine this role at the data-minimal limit by training on a single query. One-shot OPD keeps improving for hundreds of steps and recovers most of full-data OPD's gain across task domains and model families. We explain this result through the states visited during training and the rate at which the student aligns with the teacher. We measure state coverage, the fraction of the states full-data OPD visits that a query set's rollouts reach. A single query already reaches \(71.5\%\), most of it within the first 100 steps. Adding semantically distinct queries raises coverage and validation accuracy together, until 16 queries reach \(98.9\%\) and match full-data training. Yet alignment slows at a similar pace whether OPD trains on one query or the whole dataset, and even a fixed set of states takes hundreds of steps to absorb. OPD is therefore data-overfed but algorithm-starved. Its rollouts quickly expose broad supervision, while the student absorbs that supervision increasingly slowly. The state-coverage result extends to multi-teacher OPD, where 16 semantically diverse queries per domain match full-data MOPD. As a further stress test, content-light templates and off-domain WildChat queries also approach the real-query baseline. Task content and induced state coverage can therefore come apart. We hope these findings direct future work toward the step efficiency of OPD, and prompt a re-examination of the data and the mechanisms behind its recent successes in frontier post-training.

On-policy distillation (OPD) has emerged as an efficient post-training paradigm for large language models. However, standard OPD requires a live teacher inference server throughout training, resulting in substantial infrastructure overhead. In this work, we investigate whether on-policy distillation can be performed offline. A natural approach is to precompute teacher log-probabilities once over SFT rollouts and reuse them during training. In practice, however, this offline variant fails to reliably match the performance of standard OPD. To understand this discrepancy, we identify a previously overlooked condition that is critical for any OPD pipeline, which we term teacher consistency. This condition requires that the same teacher model be used for both supervised fine-tuning and OPD. We show that violating teacher consistency introduces an irreducible gradient bias, causing both offline and online OPD to converge to a suboptimal fixed point regardless of training duration. Building on this insight, we propose Lightning OPD, an offline on-policy distillation framework that enforces teacher consistency by precomputing teacher log-probabilities over SFT rollouts. This design eliminates the need for a live teacher server entirely. We further show that, under teacher consistency, Lightning OPD shares the same optimum as standard OPD, with bounded gradient discrepancy and an implicit regularization effect that helps prevent policy drift. Extensive experiments on mathematical reasoning and code generation demonstrate that Lightning OPD achieves state-of-the-art performance with significantly improved efficiency. Starting from an SFT-initialized Qwen3-8B-Base model, Lightning OPD reaches 69.9% on AIME 2024 in just 30 GPU hours, achieving a 4.0x speedup over standard OPD and substantially lowering the barrier to entry for academic research on LLM post-training.

Reinforcement learning for large language models faces a fundamental trade-off between sample efficiency and asymptotic performance: strictly on-policy methods discard trajectories after a single update, while off-policy reuse introduces distribution mismatch that existing trust-region techniques mitigate primarily by enforcing conservative optimization, often leaving rich training signals underutilized. To investigate this, we perform extensive off-policy updates on fixed data. Our experiments reveal that aggressive multi-step optimization brings rapid initial gains, but excessive updates cause trajectory probabilities to deviate and entropy to collapse, with performance plateauing early. Tightening KL constraints merely lowers the ceiling without resolving the degradation. This motivates Extreme Region Policy Distillation (ERPD), a two-stage framework that decouples sample efficiency from KL efficiency. The first stage performs weakly constrained off-policy optimization on fixed data to maximally extract training signals. The resulting policy provides token-level supervision. In the second stage, we distill these signals into the base policy under trust-region constraints, filtering harmful drift while preserving useful signals. The distilled policy achieves comparable or better performance with substantially smaller KL divergence, indicating that much of the first-stage divergence was spent on unnecessary drift rather than genuine improvement. Crucially, ERPD accommodates both strong and weak teachers: when aggressive optimization yields no stronger policy, even degenerate teachers provide effective supervision via alternative signal construction strategies. We validate ERPD on mathematical reasoning, showing gains for strong base models where on-policy training plateaus, and reliable improvements with weak teachers.

On-policy distillation (OPD) is increasingly applied to frontier foundation model post-training. Prior work in this area has largely focused on algorithmic advances, yet it remains unclear how much OPD depends on its training questions and, in particular, how far this dependence can be reduced. Across two representative single-teacher OPD settings, we find that training on 8 real prompts yields performance comparable to training on 17k problems, while datasets differing substantially in measured difficulty and initial distillation gap yield similar outcomes. Our analyses suggest two complementary explanations: repeated sampling could allow even a few prompts to expose substantial teacher supervision, while OPD transfers generalizable reasoning capabilities beyond dataset-specific knowledge. Building on these observations, we next propose a data-free on-policy distillation (DF-OPD) setting to investigate whether the system can supply the training questions itself, eliminating the need for external data. With 64 self-generated questions obtained without seed examples, DF-OPD yields performance comparable to full-data OPD in both single-teacher settings. This finding also holds in multi-teacher OPD: across mathematics, code, and instruction following, 1k generated questions achieve performance comparable to training on approximately 7k real post-training examples. We further explore whether OPD can operate even without explicit training questions. The experiments show that this is effective only in limited cases, where the student unexpectedly generates and answers its own questions, thereby reducing the process to an implicit form of DF-OPD. Together, these findings invite a reassessment of the role of training data in on-policy distillation. Code is available at https://github.com/Ryuki661/DF-OPD