Daily Papers

Generative policies based on expressive model classes, such as diffusion and flow matching, are well-suited to complex control problems with highly multimodal action distributions. Their expressivity, however, comes at a significant inference cost: generating each action typically requires simulating many steps of the generative process, compounding latency across sequential decision-making rollouts. We introduce flow map policies, a novel class of generative policies designed for fast action generation by learning to take arbitrary-size jumps including one-step jumps-across the generative dynamics of existing flow-based policies. We instantiate flow map policies for offline-to-online reinforcement learning (RL) and formulate online adaptation as a trust-region optimization problem that improves the critic's Q-value while remaining close to the offline policy. We theoretically derive FLOW MAP Q-GUIDANCE (FMQ), a principled closed-form learning target that is optimal for adapting offline flow map policies under a critic-guided trust-region constraint. We further introduce Q-GUIDED BEAM SEARCH (QGBS), a stochastic flow-map sampler that combines renoising with beam search to enable iterative inference-time refinement. Across 12 challenging robotic manipulation and locomotion tasks from OGBench and RoboMimic, FMQ achieves state-of-the-art performance in offline-to-online RL, outperforming the previous one-step policy MVP by a relative improvement of 21.3% on the average success rate.

Recent advances in flow-based offline reinforcement learning (RL) have achieved strong performance by parameterizing policies via flow matching. However, they still face critical trade-offs among expressiveness, optimality, and efficiency. In particular, existing flow policies interpret the L_2 regularization as an upper bound of the 2-Wasserstein distance (W_2), which can be problematic in offline settings. This issue stems from a fundamental geometric mismatch: the behavioral policy manifold is inherently anisotropic, whereas the L_2 (or upper bound of W_2) regularization is isotropic and density-insensitive, leading to systematically misaligned optimization directions. To address this, we revisit offline RL from a geometric perspective and show that policy refinement can be formulated as a local transport map: an initial flow policy augmented by a residual displacement. By analyzing the induced density transformation, we derive a local quadratic approximation of the KL-constrained objective governed by the Fisher information matrix, enabling a tractable anisotropic optimization formulation. By leveraging the score function embedded in the flow velocity, we obtain a corresponding quadratic constraint for efficient optimization. Our results reveal that the optimality gap in prior methods arises from their isotropic approximation. In contrast, our framework achieves a controllable approximation error within a provable neighborhood of the optimal solution. Extensive experiments demonstrate state-of-the-art performance across diverse offline RL benchmarks. See project page: https://github.com/ARC0127/Fisher-Decorator.

Offline reinforcement learning often relies on behavior regularization that enforces policies to remain close to the dataset distribution. However, such approaches fail to distinguish between high-value and low-value actions in their regularization components. We introduce Guided Flow Policy (GFP), which couples a multi-step flow-matching policy with a distilled one-step actor. The actor directs the flow policy through weighted behavior cloning to focus on cloning high-value actions from the dataset rather than indiscriminately imitating all state-action pairs. In turn, the flow policy constrains the actor to remain aligned with the dataset's best transitions while maximizing the critic. This mutual guidance enables GFP to achieve state-of-the-art performance across 144 state and pixel-based tasks from the OGBench, Minari, and D4RL benchmarks, with substantial gains on suboptimal datasets and challenging tasks. Webpage: https://simple-robotics.github.io/publications/guided-flow-policy/

Flow-based generative models, including diffusion models, excel at modeling continuous distributions in high-dimensional spaces. In this work, we introduce Flow Policy Optimization (FPO), a simple on-policy reinforcement learning algorithm that brings flow matching into the policy gradient framework. FPO casts policy optimization as maximizing an advantage-weighted ratio computed from the conditional flow matching loss, in a manner compatible with the popular PPO-clip framework. It sidesteps the need for exact likelihood computation while preserving the generative capabilities of flow-based models. Unlike prior approaches for diffusion-based reinforcement learning that bind training to a specific sampling method, FPO is agnostic to the choice of diffusion or flow integration at both training and inference time. We show that FPO can train diffusion-style policies from scratch in a variety of continuous control tasks. We find that flow-based models can capture multimodal action distributions and achieve higher performance than Gaussian policies, particularly in under-conditioned settings.

Thanks to their remarkable flexibility, diffusion models and flow models have emerged as promising candidates for policy representation. However, efficient reinforcement learning (RL) upon these policies remains a challenge due to the lack of explicit log-probabilities for vanilla policy gradient estimators. While numerous attempts have been proposed to address this, the field lacks a unified perspective to reconcile these seemingly disparate methods, thus hampering ongoing development. In this paper, we bridge this gap by introducing a comprehensive taxonomy for RL algorithms with diffusion/flow policies. To support reproducibility and agile prototyping, we introduce a modular, JAX-based open-source codebase that leverages JIT-compilation for high-throughput training. Finally, we provide systematic and standardized benchmarks across Gym-Locomotion, DeepMind Control Suite, and IsaacLab, offering a rigorous side-by-side comparison of diffusion-based methods and guidance for practitioners to choose proper algorithms based on the application. Our work establishes a clear foundation for understanding and algorithm design, a high-efficiency toolkit for future research in the field, and an algorithmic guideline for practitioners in generative models and robotics. Our code is available at https://github.com/typoverflow/flow-rl.

Few-step diffusion or flow-based generative models typically distill a velocity-predicting teacher into a student that predicts a shortcut towards denoised data. This format mismatch has led to complex distillation procedures that often suffer from a quality-diversity trade-off. To address this, we propose policy-based flow models (pi-Flow). pi-Flow modifies the output layer of a student flow model to predict a network-free policy at one timestep. The policy then produces dynamic flow velocities at future substeps with negligible overhead, enabling fast and accurate ODE integration on these substeps without extra network evaluations. To match the policy's ODE trajectory to the teacher's, we introduce a novel imitation distillation approach, which matches the policy's velocity to the teacher's along the policy's trajectory using a standard ell_2 flow matching loss. By simply mimicking the teacher's behavior, pi-Flow enables stable and scalable training and avoids the quality-diversity trade-off. On ImageNet 256^2, it attains a 1-NFE FID of 2.85, outperforming MeanFlow of the same DiT architecture. On FLUX.1-12B and Qwen-Image-20B at 4 NFEs, pi-Flow achieves substantially better diversity than state-of-the-art few-step methods, while maintaining teacher-level quality.

Recent advances in diffusion/flow-matching policies have enabled imitation learning of complex, multi-modal action trajectories. However, they are computationally expensive because they sample a trajectory of trajectories: a diffusion/flow trajectory of action trajectories. They discard intermediate action trajectories, and must wait for the sampling process to complete before any actions can be executed on the robot. We simplify diffusion/flow policies by treating action trajectories as flow trajectories. Instead of starting from pure noise, our algorithm samples from a narrow Gaussian around the last action. Then, it incrementally integrates a velocity field learned via flow matching to produce a sequence of actions that constitute a single trajectory. This enables actions to be streamed to the robot on-the-fly during the flow sampling process, and is well-suited for receding horizon policy execution. Despite streaming, our method retains the ability to model multi-modal behavior. We train flows that stabilize around demonstration trajectories to reduce distribution shift and improve imitation learning performance. Streaming flow policy outperforms prior methods while enabling faster policy execution and tighter sensorimotor loops for learning-based robot control. Project website: https://streaming-flow-policy.github.io/

Among on-policy reinforcement learning algorithms, Proximal Policy Optimization (PPO) demonstrates is widely favored for its simplicity, numerical stability, and strong empirical performance. Standard PPO relies on surrogate objectives defined via importance ratios, which require evaluating policy likelihood that is typically straightforward when the policy is modeled as a Gaussian distribution. However, extending PPO to more expressive, high-capacity policy models such as continuous normalizing flows (CNFs), also known as flow-matching models, is challenging because likelihood evaluation along the full flow trajectory is computationally expensive and often numerically unstable. To resolve this issue, we propose PolicyFlow, a novel on-policy CNF-based reinforcement learning algorithm that integrates expressive CNF policies with PPO-style objectives without requiring likelihood evaluation along the full flow path. PolicyFlow approximates importance ratios using velocity field variations along a simple interpolation path, reducing computational overhead without compromising training stability. To further prevent mode collapse and further encourage diverse behaviors, we propose the Brownian Regularizer, an implicit policy entropy regularizer inspired by Brownian motion, which is conceptually elegant and computationally lightweight. Experiments on diverse tasks across various environments including MultiGoal, PointMaze, IsaacLab and MuJoCo Playground show that PolicyFlow achieves competitive or superior performance compared to PPO using Gaussian policies and flow-based baselines including FPO and DPPO. Notably, results on MultiGoal highlight PolicyFlow's ability to capture richer multimodal action distributions.

Few-step video generation has been significantly advanced by consistency distillation. However, the performance of consistency-distilled models often degrades as more sampling steps are allocated at test time, limiting their effectiveness for any-step video diffusion. This limitation arises because consistency distillation replaces the original probability-flow ODE trajectory with a consistency-sampling trajectory, weakening the desirable test-time scaling behavior of ODE sampling. To address this limitation, we introduce AnyFlow, the first any-step video diffusion distillation framework based on flow maps. Instead of distilling a model for only a few fixed sampling steps, AnyFlow optimizes the full ODE sampling trajectory. To this end, we shift the distillation target from endpoint consistency mapping (z_{t}rightarrow z_{0}) to flow-map transition learning (z_{t}rightarrow z_{r}) over arbitrary time intervals. We further propose Flow Map Backward Simulation, which decomposes a full Euler rollout into shortcut flow-map transitions, enabling efficient on-policy distillation that reduces test-time errors (i.e., discretization error in few-step sampling and exposure bias in causal generation). Extensive experiments across both bidirectional and causal architectures, at scales ranging from 1.3B to 14B parameters, demonstrate that AnyFlow achieves performance matches or surpasses consistency-based counterparts in the few-step regime, while scaling with sampling step budgets.

Outcome-driven reinforcement learning has advanced reasoning in large language models (LLMs), but prevailing tool-augmented approaches train a single, monolithic policy that interleaves thoughts and tool calls under full context; this scales poorly with long horizons and diverse tools and generalizes weakly to new scenarios. Agentic systems offer a promising alternative by decomposing work across specialized modules, yet most remain training-free or rely on offline training decoupled from the live dynamics of multi-turn interaction. We introduce AgentFlow, a trainable, in-the-flow agentic framework that coordinates four modules (planner, executor, verifier, generator) through an evolving memory and directly optimizes its planner inside the multi-turn loop. To train on-policy in live environments, we propose Flow-based Group Refined Policy Optimization (Flow-GRPO), which tackles long-horizon, sparse-reward credit assignment by converting multi-turn optimization into a sequence of tractable single-turn policy updates. It broadcasts a single, verifiable trajectory-level outcome to every turn to align local planner decisions with global success and stabilizes learning with group-normalized advantages. Across ten benchmarks, AgentFlow with a 7B-scale backbone outperforms top-performing baselines with average accuracy gains of 14.9% on search, 14.0% on agentic, 14.5% on mathematical, and 4.1% on scientific tasks, even surpassing larger proprietary models like GPT-4o. Further analyses confirm the benefits of in-the-flow optimization, showing improved planning, enhanced tool-calling reliability, and positive scaling with model size and reasoning turns.

There is growing interest in utilizing flow-based models as decision-making policies in reinforcement learning due to their high expressive capacity. However, effectively leveraging this expressivity for value maximization remains challenging, as naive gradient-based optimization requires backpropagating through numerical solvers and often leads to instability. Existing approaches typically address this issue by restricting the expressive capacity of flow-based policies, resulting in a trade-off between optimization stability and representational flexibility. To resolve this, we introduce Q-Flow, a framework that leverages the deterministic nature of flow dynamics to explicitly propagate terminal trajectory value to intermediate latent states along the policy-induced flow. This formulation enables stable policy optimization using intermediate value gradients without unrolling the numerical solver, effectively bridging the gap between stability and expressivity. We evaluate Q-Flow in the offline learning setting on the challenging OGBench suite, where it consistently outperforms state-of-the-art baselines by an average of 10.6 percentage points, while also enabling stable online adaptation within the same framework.

Vision-language-action (VLA) models have shown remarkable capabilities in robotic manipulation, but their performance is sensitive to the action chunk length used during training, termed horizon. Our empirical study reveals an inherent trade-off: longer horizons provide stronger global foresight but degrade fine-grained accuracy, while shorter ones sharpen local control yet struggle on long-term tasks, implying fixed choice of single horizons being suboptimal. To mitigate the trade-off, we propose a mixture of horizons (MoH) strategy. MoH rearranges the action chunk into several segments with different horizons, processes them in parallel with a shared action transformer, and fuses outputs with a light linear gate. It has three appealing benefits. 1) MoH exploits long-term foresight and short-term precision jointly within a single model, improving both performance and generalizability to complex tasks. 2) MoH is plug-and-play for full-attention action modules with minimal training or inference overhead. 3) MoH enables dynamic inference with adaptive horizons, which selects stable actions through cross-horizon consensus, achieving 2.5times higher throughput than baselines while preserving superior performance. Extensive experiments over flow-based policies π_0, π_{0.5}, and one-step regression policy π_{reg} demonstrate that MoH yields consistent and significant gains on both simulations and real-world tasks. Notably, under mixed-task setting, π_{0.5} with MoH reaches a new state-of-the-art with 99% average success rate on LIBERO after only 30k training iterations. Project page: https://github.com/Timsty1/MixtureOfHorizons

Flow-based generative models achieve state-of-the-art sample quality, but require the expensive solution of a differential equation at inference time. Flow map models, commonly known as consistency models, encompass many recent efforts to improve inference-time efficiency by learning the solution operator of this differential equation. Yet despite their promise, these models lack a unified description that clearly explains how to learn them efficiently in practice. Here, building on the methodology proposed in Boffi et. al. (2024), we present a systematic algorithmic framework for directly learning the flow map associated with a flow or diffusion model. By exploiting a relationship between the velocity field underlying a continuous-time flow and the instantaneous rate of change of the flow map, we show how to convert any distillation scheme into a direct training algorithm via self-distillation, eliminating the need for pre-trained teachers. We introduce three algorithmic families based on different mathematical characterizations of the flow map: Eulerian, Lagrangian, and Progressive methods, which we show encompass and extend all known distillation and direct training schemes for consistency models. We find that the novel class of Lagrangian methods, which avoid both spatial derivatives and bootstrapping from small steps by design, achieve significantly more stable training and higher performance than more standard Eulerian and Progressive schemes. Our methodology unifies existing training schemes under a single common framework and reveals new design principles for accelerated generative modeling. Associated code is available at https://github.com/nmboffi/flow-maps.

Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch, motivating subsequent work to explain and stabilize these issues. While these efforts have provided valuable insights, the explanations remain fragmented, and the theoretical relationships remain unclear. In this work, we provide a theoretical examination of consistency models by analyzing them from a flow map-based perspective. This joint analysis clarifies how training stability and convergence behavior can give rise to degenerate solutions. Building on these insights, we revisit self-distillation as a practical remedy for certain forms of suboptimal convergence and reformulate it to avoid excessive gradient norms for stable optimization. We further demonstrate that our strategy extends beyond image generation to diffusion-based policy learning, without reliance on a pretrained diffusion model for initialization, thereby illustrating its broader applicability.

We propose ReinFlow, a simple yet effective online reinforcement learning (RL) framework that fine-tunes a family of flow matching policies for continuous robotic control. Derived from rigorous RL theory, ReinFlow injects learnable noise into a flow policy's deterministic path, converting the flow into a discrete-time Markov Process for exact and straightforward likelihood computation. This conversion facilitates exploration and ensures training stability, enabling ReinFlow to fine-tune diverse flow model variants, including Rectified Flow [35] and Shortcut Models [19], particularly at very few or even one denoising step. We benchmark ReinFlow in representative locomotion and manipulation tasks, including long-horizon planning with visual input and sparse reward. The episode reward of Rectified Flow policies obtained an average net growth of 135.36% after fine-tuning in challenging legged locomotion tasks while saving denoising steps and 82.63% of wall time compared to state-of-the-art diffusion RL fine-tuning method DPPO [43]. The success rate of the Shortcut Model policies in state and visual manipulation tasks achieved an average net increase of 40.34% after fine-tuning with ReinFlow at four or even one denoising step, whose performance is comparable to fine-tuned DDIM policies while saving computation time for an average of 23.20%. Project webpage: https://reinflow.github.io/

Transport maps can ease the sampling of distributions with non-trivial geometries by transforming them into distributions that are easier to handle. The potential of this approach has risen with the development of Normalizing Flows (NF) which are maps parameterized with deep neural networks trained to push a reference distribution towards a target. NF-enhanced samplers recently proposed blend (Markov chain) Monte Carlo methods with either (i) proposal draws from the flow or (ii) a flow-based reparametrization. In both cases, the quality of the learned transport conditions performance. The present work clarifies for the first time the relative strengths and weaknesses of these two approaches. Our study concludes that multimodal targets can be reliably handled with flow-based proposals up to moderately high dimensions. In contrast, methods relying on reparametrization struggle with multimodality but are more robust otherwise in high-dimensional settings and under poor training. To further illustrate the influence of target-proposal adequacy, we also derive a new quantitative bound for the mixing time of the Independent Metropolis-Hastings sampler.

A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed, as user-specified rewards are usually only well defined on the data distribution at the end of generation. While common workarounds to this problem are to use a denoiser to estimate what a sample would have been at the end of generation, we propose a simple solution to this problem by working directly with a flow map. By exploiting a relationship between the flow map and velocity field governing the instantaneous transport, we construct an algorithm, Flow Map Trajectory Tilting (FMTT), which provably performs better ascent on the reward than standard test-time methods involving the gradient of the reward. The approach can be used to either perform exact sampling via importance weighting or principled search that identifies local maximizers of the reward-tilted distribution. We demonstrate the efficacy of our approach against other look-ahead techniques, and show how the flow map enables engagement with complicated reward functions that make possible new forms of image editing, e.g. by interfacing with vision language models.

Diffusion- and flow-based models have emerged as state-of-the-art generative modeling approaches, but they require many sampling steps. Consistency models can distill these models into efficient one-step generators; however, unlike flow- and diffusion-based methods, their performance inevitably degrades when increasing the number of steps, which we show both analytically and empirically. Flow maps generalize these approaches by connecting any two noise levels in a single step and remain effective across all step counts. In this paper, we introduce two new continuous-time objectives for training flow maps, along with additional novel training techniques, generalizing existing consistency and flow matching objectives. We further demonstrate that autoguidance can improve performance, using a low-quality model for guidance during distillation, and an additional boost can be achieved by adversarial finetuning, with minimal loss in sample diversity. We extensively validate our flow map models, called Align Your Flow, on challenging image generation benchmarks and achieve state-of-the-art few-step generation performance on both ImageNet 64x64 and 512x512, using small and efficient neural networks. Finally, we show text-to-image flow map models that outperform all existing non-adversarially trained few-step samplers in text-conditioned synthesis.

Self-conditioning is a core technique that enhances continuous flow-based language models, where the model learns to denoise generated text by conditioning on its own denoising estimate. While empirically successful, its performance improvements are poorly understood. Moreover, there is growing interest in the use of few-step generators based on flow maps, for which how to leverage self-conditioning is unclear. Here, we show that flow language models with self-conditioning solve a fixed-point iteration that bootstraps the performance of the learned denoiser. We use this viewpoint to formulate fixed-point flows, a two-dimensional class of self-conditioned flows, where the first dimension represents the flow process and the second represents the fixed-point iteration. We show that fixed-point flows define valid flow maps, and show that they can be distilled from self-conditioned flow models by compressing both fixed-point iterations and the flow process, the former with fixed-point distillation and the latter with flow map distillation. Our resulting flow map language model, FMLM^star, outperforms state-of-the-art self-conditioned models and few-step models in one- and few-step generation on OpenWebText. Code is available at https://github.com/Ugness/self-conditioned-fmlm.

Training expressive flow-based policies with off-policy reinforcement learning is notoriously unstable due to gradient pathologies in the multi-step action sampling process. We trace this instability to a fundamental connection: the flow rollout is algebraically equivalent to a residual recurrent computation, making it susceptible to the same vanishing and exploding gradients as RNNs. To address this, we reparameterize the velocity network using principles from modern sequential models, introducing two stable architectures: Flow-G, which incorporates a gated velocity, and Flow-T, which utilizes a decoded velocity. We then develop a practical SAC-based algorithm, enabled by a noise-augmented rollout, that facilitates direct end-to-end training of these policies. Our approach supports both from-scratch and offline-to-online learning and achieves state-of-the-art performance on continuous control and robotic manipulation benchmarks, eliminating the need for common workarounds like policy distillation or surrogate objectives.

Traditional customer support systems, such as Interactive Voice Response (IVR), rely on rigid scripts and lack the flexibility required for handling complex, policy-driven tasks. While large language model (LLM) agents offer a promising alternative, evaluating their ability to act in accordance with business rules and real-world support workflows remains an open challenge. Existing benchmarks primarily focus on tool usage or task completion, overlooking an agent's capacity to adhere to multi-step policies, navigate task dependencies, and remain robust to unpredictable user or environment behavior. In this work, we introduce JourneyBench, a benchmark designed to assess policy-aware agents in customer support. JourneyBench leverages graph representations to generate diverse, realistic support scenarios and proposes the User Journey Coverage Score, a novel metric to measure policy adherence. We evaluate multiple state-of-the-art LLMs using two agent designs: a Static-Prompt Agent (SPA) and a Dynamic-Prompt Agent (DPA) that explicitly models policy control. Across 703 conversations in three domains, we show that DPA significantly boosts policy adherence, even allowing smaller models like GPT-4o-mini to outperform more capable ones like GPT-4o. Our findings demonstrate the importance of structured orchestration and establish JourneyBench as a critical resource to advance AI-driven customer support beyond IVR-era limitations.

A flow control system is a critical concept for increasing the production capacity of manufacturing systems. To solve the scheduling optimization problem related to the flow control with the aim of improving productivity, existing methods depend on a heuristic design by domain human experts. Therefore, the methods require correction, monitoring, and verification by using real equipment. As system designs increase in complexity, the monitoring time increases, which decreases the probability of arriving at the optimal design. As an alternative approach to the heuristic design of flow control systems, the use of deep reinforcement learning to solve the scheduling optimization problem has been considered. Although the existing research on reinforcement learning has yielded excellent performance in some areas, the applicability of the results to actual FAB such as display and semiconductor manufacturing processes is not evident so far. To this end, we propose a method to implement a physical simulation environment and devise a feasible flow control system design using a transfer robot in display manufacturing through reinforcement learning. We present a model and parameter setting to build a virtual environment for different display transfer robots, and training methods of reinforcement learning on the environment to obtain an optimal scheduling of glass flow control systems. Its feasibility was verified by using different types of robots used in the actual process.

We propose Flow-Anchored Noise-conditioned Q-Learning (FAN), a highly efficient and high-performing offline reinforcement learning (RL) algorithm. Recent work has shown that expressive flow policies and distributional critics improve offline RL performance, but at a high computational cost. Specifically, flow policies require iterative sampling to produce a single action, and distributional critics require computation over multiple samples (e.g., quantiles) to estimate value. To address these inefficiencies while maintaining high performance, we introduce FAN. Our method employs a behavior regularization technique that utilizes only a single flow policy iteration and requires only a single Gaussian noise sample for distributional critics. Our theoretical analysis of convergence and performance bounds demonstrates that these simplifications not only improve efficiency but also lead to superior task performance. Experiments on robotic manipulation and locomotion tasks demonstrate that FAN achieves state-of-the-art performance while significantly reducing both training and inference runtimes. We release our code at https://github.com/brianlsy98/FAN.

Classifier-free guidance is a key component for enhancing the performance of conditional generative models across diverse tasks. While it has previously demonstrated remarkable improvements for the sample quality, it has only been exclusively employed for diffusion models. In this paper, we integrate classifier-free guidance into Flow Matching (FM) models, an alternative simulation-free approach that trains Continuous Normalizing Flows (CNFs) based on regressing vector fields. We explore the usage of Guided Flows for a variety of downstream applications. We show that Guided Flows significantly improves the sample quality in conditional image generation and zero-shot text-to-speech synthesis, boasting state-of-the-art performance. Notably, we are the first to apply flow models for plan generation in the offline reinforcement learning setting, showcasing a 10x speedup in computation compared to diffusion models while maintaining comparable performance.

Iterative generative modeling techniques, such as flow matching, provide powerful tools to model complex behaviors for effective offline reinforcement learning (RL). In this work, we propose a new off-policy RL algorithm that trains a flow policy based on prior data. Our idea starts from the "expanded" Markov decision process (MDP) framework, which treats individual flow refinement steps as separate actions in an MDP. To enable off-policy RL within this framework, we apply two techniques: we generate virtual on-policy trajectories (by "reversing" flows) to make this framework compatible with prior data, and we apply a bias-and-variance reduction technique to mitigate the curse of horizon in off-policy RL. We call the resulting algorithm Reversal Q-learning (RQL). RQL has several advantages over previous flow-based RL methods: it does not suffer from backpropagation through time, makes better use of the learned value function, and directly trains the full, expressive flow policy. Through our experiments on 50 challenging simulated robotic tasks, we show that RQL leads to the best average offline RL performance compared to state-of-the-art flow-based offline RL algorithms.

Generative models, like flows and diffusions, have recently emerged as popular and efficacious policy parameterizations in robotics. There has been much speculation as to the factors underlying their successes, ranging from capturing multi-modal action distribution to expressing more complex behaviors. In this work, we perform a comprehensive evaluation of popular generative control policies (GCPs) on common behavior cloning (BC) benchmarks. We find that GCPs do not owe their success to their ability to capture multi-modality or to express more complex observation-to-action mappings. Instead, we find that their advantage stems from iterative computation, as long as intermediate steps are supervised during training and this supervision is paired with a suitable level of stochasticity. As a validation of our findings, we show that a minimum iterative policy (MIP), a lightweight two-step regression-based policy, essentially matches the performance of flow GCPs, and often outperforms distilled shortcut models. Our results suggest that the distribution-fitting component of GCPs is less salient than commonly believed, and point toward new design spaces focusing solely on control performance. Project page: https://simchowitzlabpublic.github.io/much-ado-about-noising-project/

Expressive continuous control policies, such as diffusion and flow models, form the backbone of recent advances in scaling imitation learning for simulated and real robot control. While they are known to scale stably in the supervised imitation learning setting, incorporating them into reinforcement learning (RL) pipelines for policy improvement has proven more difficult. It often requires specialized training objectives or backpropagating through denoising processes, which cause well-known issues with stability and affect scalability. In this paper we study the question of whether simple policy improvement schemes at test time alone, leaving stable supervised policy training intact, can be a competitive alternative which sidesteps these issues. To this end, we propose QGF (Q-Guided Flow), an RL algorithm that performs policy optimization entirely at test time. QGF works by pre-training both a reference flow policy (via a standard behavioral cloning objective) and a value function critic and, at test time, using the value gradient to guide the reference policy to generate higher-value actions without any additional policy learning. Empirically, QGF outperforms prior test-time RL methods on single-task and goal-conditioned offline RL benchmarks with high-dimensional action spaces, and is competitive with state-of-the-art training-time algorithms while being much cheaper to run. Moreover, it exhibits favorable scaling with model size by avoiding the instability of actor-critic training, offering a practical and effective alternative RL algorithm with expressive policies.

Flow map models such as Consistency Models (CM) and Mean Flow (MF) enable few-step generation by learning the long jump of the ODE solution of diffusion models, yet training remains unstable, sensitive to hyperparameters, and costly. Initializing from a pre-trained diffusion model helps, but still requires converting infinitesimal steps into a long-jump map, leaving instability unresolved. We introduce mid-training, the first concept and practical method that inserts a lightweight intermediate stage between the (diffusion) pre-training and the final flow map training (i.e., post-training) for vision generation. Concretely, Consistency Mid-Training (CMT) is a compact and principled stage that trains a model to map points along a solver trajectory from a pre-trained model, starting from a prior sample, directly to the solver-generated clean sample. It yields a trajectory-consistent and stable initialization. This initializer outperforms random and diffusion-based baselines and enables fast, robust convergence without heuristics. Initializing post-training with CMT weights further simplifies flow map learning. Empirically, CMT achieves state of the art two step FIDs: 1.97 on CIFAR-10, 1.32 on ImageNet 64x64, and 1.84 on ImageNet 512x512, while using up to 98% less training data and GPU time, compared to CMs. On ImageNet 256x256, CMT reaches 1-step FID 3.34 while cutting total training time by about 50% compared to MF from scratch (FID 3.43). This establishes CMT as a principled, efficient, and general framework for training flow map models.

Reinforcement learning (RL) has shown promising results in active flow control (AFC), yet progress in the field remains difficult to assess as existing studies rely on heterogeneous observation and actuation schemes, numerical setups, and evaluation protocols. Current AFC benchmarks attempt to address these issues but heavily rely on external computational fluid dynamics (CFD) solvers, are not fully differentiable, and provide limited 3D and multi-agent support. To overcome these limitations, we introduce FluidGym, the first standalone, fully differentiable benchmark suite for RL in AFC. Built entirely in PyTorch on top of the GPU-accelerated PICT solver, FluidGym runs in a single Python stack, requires no external CFD software, and provides standardized evaluation protocols. We present baseline results with PPO and SAC and release all environments, datasets, and trained models as public resources. FluidGym enables systematic comparison of control methods, establishes a scalable foundation for future research in learning-based flow control, and is available at https://github.com/safe-autonomous-systems/fluidgym.

Generative flow and diffusion models provide the continuous, multimodal action distributions needed for high-precision robotic policies. However, their reliance on iterative sampling introduces severe inference latency, degrading control frequency and harming performance in time-sensitive manipulation. To address this problem, we propose the One-Step Flow Policy (OFP), a from-scratch self-distillation framework for high-fidelity, single-step action generation without a pre-trained teacher. OFP unifies a self-consistency loss to enforce coherent transport across time intervals, and a self-guided regularization to sharpen predictions toward high-density expert modes. In addition, a warm-start mechanism leverages temporal action correlations to minimize the generative transport distance. Evaluations across 56 diverse simulated manipulation tasks demonstrate that a one-step OFP achieves state-of-the-art results, outperforming 100-step diffusion and flow policies while accelerating action generation by over 100times. We further integrate OFP into the π_{0.5} model on RoboTwin 2.0, where one-step OFP surpasses the original 10-step policy. These results establish OFP as a practical, scalable solution for highly accurate and low-latency robot control.

Deep research is an inherently challenging task that demands both breadth and depth of thinking. It involves navigating diverse knowledge spaces and reasoning over complex, multi-step dependencies, which presents substantial challenges for agentic systems. To address this, we propose FlowSearch, a multi-agent framework that actively constructs and evolves a dynamic structured knowledge flow to drive subtask execution and reasoning. FlowSearch is capable of strategically planning and expanding the knowledge flow to enable parallel exploration and hierarchical task decomposition, while also adjusting the knowledge flow in real time based on feedback from intermediate reasoning outcomes and insights. FlowSearch achieves state-of-the-art performance on both general and scientific benchmarks, including GAIA, HLE, GPQA and TRQA, demonstrating its effectiveness in multi-disciplinary research scenarios and its potential to advance scientific discovery. The code is available at https://github.com/Alpha-Innovator/InternAgent.

Aligning generative flow models on continuous spaces via online reinforcement learning is constrained by intractable trajectory likelihoods. Existing density-approximated policy gradient methods rely on stochastic SDE samplers to construct tractable transition kernels, which introduce training-inference inconsistencies and necessitates Classifier-Free Guidance (CFG). While implicit frameworks such as DiffusionNFT directly optimize forward-process velocity fields, its heuristic fixed-magnitude corrections prevent optimization strength from relative intra-group quality. We propose Flow Advantage-Weighted Rectification (FlowAWR), a paradigm that recasts continuous generative policy optimization as supervised regression toward a theoretically optimal velocity field. Starting from the optimal policy of a KL-constrained reward maximization, FlowAWR derives the optimal velocity field that admits a magnitude-aware, advantage-weighted rectification form, yielding SDE-free optimization and CFG-free generation. In comparative evaluations on SD3.5-Medium, FlowAWR achieves improved alignment performance alongside a 2times to 5times convergence acceleration over DiffusionNFT (e.g., reaching a 24.12 PickScore in 1.2k steps, versus 23.82 in 2.0k steps for DiffusionNFT and 23.50 in >4k steps for FlowGRPO). Under multi-reward constraints, FlowAWR sustains generation quality, satisfying structural rules while maintaining stable out-of-domain performance.

Off-policy reinforcement learning of pretrained flow policies remains challenging due to the instability of optimization arising from the multi-step sampling process. Recently, Q-learning with Adjoint Matching (QAM) addressed this issue by reformulating into a memoryless stochastic optimal control (SOC) problem with a learned critic. However, QAM inherits a fundamental fragility of critic-guided improvement: small critic errors are amplified when critics are ill-conditioned, often leading to model collapse. This paper introduces Trust Region Q-Adjoint Matching (TRQAM), a stable off-policy fine-tuning algorithm that adaptively controls the path-space KL with pretrained flow policies through projected dual descent. Specifically, we optimize the trust-region parameter λ in SOC dynamics, and theoretically show that the path-space KL can be represented by a closed-form function of λ. As a result, our method can precisely control the exact deviation from pretrained flow policies, achieving stable off-policy RL. Through experiments on 50 OGBench tasks, TRQAM consistently outperforms prior arts in both offline RL and offline-to-online RL. In particular, TRQAM achieves an overall success rate of 68% in offline RL, substantially improves the strongest baseline at 46%.

Offline reinforcement learning requires improving a policy from fixed data while avoiding out-of-distribution actions with unreliable value estimates. Diffusion and flow policies handle this trade-off by modeling the behavior distribution to regularize the RL objective, but they require iterative denoising, solver integrations, and in more efficient variants, distillation or other approximations at inference. We propose DriftQL, which combines a drift-based behavioral regularizer with critic-driven policy improvement. The value signal biases the policy toward high-value regions of the data support, while attraction and repulsion together keep generated actions near the data and prevent collapse onto a single mode. DriftQL is implemented as a single network with a unified training objective and generates actions in a single forward pass. On D4RL and OGBench, DriftQL consistently outperforms diffusion and flow methods, advancing the state of the art. Under degraded data quality, where the baselines visibly struggle, DriftQL remains close to its clean-data performance, positioning it as a promising alternative to diffusion and flow-based methods while maintaining the simplicity and efficiency of deterministic approaches. Project page: https://driftql.github.io/

Recent work has demonstrated that online reinforcement learning (RL) can substantially improve the quality and alignment of flow matching models for image and video generation. Methods such as Flow-GRPO and CPS cast the denoising process as a Markov Decision Process and apply PPO-style ratio clipping to enforce a trust region. However, we argue that ratio clipping is structurally ill-suited for flow models: the probability ratio between new and old policies is a noisy, single-sample estimate of the true policy divergence, leading to over-constraining in some regions of the trajectory and under-constraining in others. We propose Flow-DPPO (Flow Divergence Proximal Policy Optimization), which replaces ratio clipping with a divergence proximal constraint. A key observation is that the per-step policy in flow models is Gaussian, enabling exact and cheap computation of the KL divergence between old and new policies. Flow-DPPO employs an asymmetric divergence mask that blocks gradient updates only when they simultaneously move away from the trusted region and violate the divergence threshold. Experiments show that Flow-DPPO achieves higher rewards with better KL-proximal efficiency, alleviates catastrophic forgetting, promotes balanced multi-objective optimization, and enables stable multi-epoch training where ratio clipping degrades. Code and models are available at https://github.com/Tencent-Hunyuan/UniRL/tree/main/FlowDPPO.

Existing Flow Matching (FM) text-to-image models suffer from two critical bottlenecks under multi-task alignment: the reward sparsity induced by scalar-valued rewards, and the gradient interference arising from jointly optimizing heterogeneous objectives, which together give rise to a 'seesaw effect' of competing metrics and pervasive reward hacking. Inspired by the success of On-Policy Distillation (OPD) in the large language model community, we propose Flow-OPD, the first unified post-training framework that integrates on-policy distillation into Flow Matching models. Flow-OPD adopts a two-stage alignment strategy: it first cultivates domain-specialized teacher models via single-reward GRPO fine-tuning, allowing each expert to reach its performance ceiling in isolation; it then establishes a robust initial policy through a Flow-based Cold-Start scheme and seamlessly consolidates heterogeneous expertise into a single student via a three-step orchestration of on-policy sampling, task-routing labeling, and dense trajectory-level supervision. We further introduce Manifold Anchor Regularization (MAR), which leverages a task-agnostic teacher to provide full-data supervision that anchors generation to a high-quality manifold, effectively mitigating the aesthetic degradation commonly observed in purely RL-driven alignment. Built upon Stable Diffusion 3.5 Medium, Flow-OPD raises the GenEval score from 63 to 92 and the OCR accuracy from 59 to 94, yielding an overall improvement of roughly 10 points over vanilla GRPO, while preserving image fidelity and human-preference alignment and exhibiting an emergent 'teacher-surpassing' effect. These results establish Flow-OPD as a scalable alignment paradigm for building generalist text-to-image models.

Flow-GRPO successfully applies reinforcement learning to flow models, but uses uniform credit assignment across all steps. This ignores the temporal structure of diffusion generation: early steps determine composition and content (low-frequency structure), while late steps resolve details and textures (high-frequency details). Moreover, assigning uniform credit based solely on the final image can inadvertently reward suboptimal intermediate steps, especially when errors are corrected later in the diffusion trajectory. We propose Stepwise-Flow-GRPO, which assigns credit based on each step's reward improvement. By leveraging Tweedie's formula to obtain intermediate reward estimates and introducing gain-based advantages, our method achieves superior sample efficiency and faster convergence. We also introduce a DDIM-inspired SDE that improves reward quality while preserving stochasticity for policy gradients.

Denoising generative models, such as diffusion and flow-based models, produce high-quality samples but require many denoising steps due to discretization error. Flow maps, which estimate the average velocity between timesteps, mitigate this error and enable faster sampling. However, their training typically demands architectural changes that limit compatibility with pretrained flow models. We introduce Decoupled MeanFlow, a simple decoding strategy that converts flow models into flow map models without architectural modifications. Our method conditions the final blocks of diffusion transformers on the subsequent timestep, allowing pretrained flow models to be directly repurposed as flow maps. Combined with enhanced training techniques, this design enables high-quality generation in as few as 1 to 4 steps. Notably, we find that training flow models and subsequently converting them is more efficient and effective than training flow maps from scratch. On ImageNet 256x256 and 512x512, our models attain 1-step FID of 2.16 and 2.12, respectively, surpassing prior art by a large margin. Furthermore, we achieve FID of 1.51 and 1.68 when increasing the steps to 4, which nearly matches the performance of flow models while delivering over 100x faster inference.

Group Relative Policy Optimization (GRPO) has demonstrated remarkable success in aligning text-to-image (T2I) flow models with human preferences. However, we have identified that the learning loop of current flow-based GRPO is fundamentally decoupled from the learner's current capability, suffering from critical blind spots at both prompt selection and advantage estimation: (i) Existing methods sample prompts randomly, overlooking the substantial impact of data selection on reinforcement learning (RL) efficacy--a factor proven crucial in GRPO for large language models; (ii) They evaluate sample quality solely relying on intra-group statistics, lacking a global perspective to accurately measure true policy improvement. To address these issues, we propose Adaptive GRPO (AdaGRPO), a novel capability-aware RL algorithm tailored for flow models. Specifically, AdaGRPO consists of two principal components: (i) Online Curriculum Filtering Strategy: Dynamically tracks the model's proficiency and adaptively selects prompts that best match its current learning boundary; (ii) Cross-Level Advantage Fusion: Synergistically integrates fine-grained intra-group advantages with macro-level global advantages, providing a comprehensive and unbiased policy evaluation. As a lightweight, plug-and-play module, AdaGRPO can be seamlessly integrated with existing frameworks such as Flow-GRPO, DanceGRPO, and Flow-CPS. Extensive experiments demonstrate that AdaGRPO consistently drives performance gains while significantly stabilizes GRPO training for flow models.

Flowcharts are a critical tool for visualizing decision-making processes. However, their non-linear structure and complex visual-textual relationships make it challenging to interpret them using LLMs, as vision-language models frequently hallucinate nonexistent connections and decision paths when analyzing these diagrams. This leads to compromised reliability for automated flowchart processing in critical domains such as logistics, health, and engineering. We introduce the task of Fine-grained Flowchart Attribution, which traces specific components grounding a flowchart referring LLM response. Flowchart Attribution ensures the verifiability of LLM predictions and improves explainability by linking generated responses to the flowchart's structure. We propose FlowPathAgent, a neurosymbolic agent that performs fine-grained post hoc attribution through graph-based reasoning. It first segments the flowchart, then converts it into a structured symbolic graph, and then employs an agentic approach to dynamically interact with the graph, to generate attribution paths. Additionally, we present FlowExplainBench, a novel benchmark for evaluating flowchart attributions across diverse styles, domains, and question types. Experimental results show that FlowPathAgent mitigates visual hallucinations in LLM answers over flowchart QA, outperforming strong baselines by 10-14% on our proposed FlowExplainBench dataset.

Large Language Model (LLM)-based agentic systems rely on in-context policy documents encoding diverse business rules. As requirements grow, these documents expand rapidly, causing high computational overhead. This motivates developing internalization methods that embed policy documents into model priors while preserving performance. Prior prompt compression work targets generic prompts, but agentic policy documents span multiple complexity levels and require deeper reasoning, making internalization harder. We introduce CC-Gen, an agentic benchmark generator with Controllable Complexity across four levels, enabling systematic evaluation of agents' ability to handle complexity and offering a unified framework for assessing policy internalization. Our analysis shows that complex policy specifications governing workflows pose major reasoning challenges. Supporting internalization with gold user agent interaction trajectories containing chain-of-thought (CoT) annotations via supervised fine-tuning (SFT) is data-intensive and degrades sharply as policy complexity increases. To mitigate data and reasoning burdens, we propose Category-Aware Policy Continued Pretraining (CAP-CPT). Our automated pipeline parses policy documents to extract key specifications, grouping them into factual, behavioral, and conditional categories, and isolating complex conditions that drive workflow complexity. This guides targeted data synthesis and enables agents to internalize policy information through an autoregressive pretraining loss. Experiments show CAP-CPT improves SFT baselines in all settings, with up to 41% and 22% gains on Qwen-3-32B, achieving 97.3% prompt length reduction on CC-Gen and further enhancing tau-Bench with minimal SFT data.

Flow and diffusion models generate high-quality samples in many modalities; however, many network evaluations are required during inference due to numerical integration of an underlying differential equation. Flow maps alleviate this problem by learning the solution map of the differential equation directly, enabling few-step sampling. Yet, current methods are restricted to approximating the solution map of ODEs. These methods can be used to learn the transition kernel of an SDE, thereby obtaining a solution map that recovers the marginal distributions of the process (weak convergence) rather than the solution path (strong convergence). We propose Strong Stochastic Flow Maps (SSFMs) as a novel framework for learning the strong solution map of additive-noise SDEs, directly generalizing deterministic flow maps to the stochastic setting. Further, a polynomial approximation to Brownian motion is introduced and shown to converge pathwise. These results enable a simulation-free training objective for the solution map of diffusion models. We demonstrate that SSFMs outperform previous stochastic flow map methods on image generation and enable few-step sampling of molecular systems.

We introduce a one-step generative policy for offline reinforcement learning that maps noise directly to actions via a residual reformulation of MeanFlow, making it compatible with Q-learning. While one-step Gaussian policies enable fast inference, they struggle to capture complex, multimodal action distributions. Existing flow-based methods improve expressivity but typically rely on distillation and two-stage training when trained with Q-learning. To overcome these limitations, we propose to reformulate MeanFlow to enable direct noise-to-action generation by integrating the velocity field and noise-to-action transformation into a single policy network-eliminating the need for separate velocity estimation. We explore several reformulation variants and identify an effective residual formulation that supports expressive and stable policy learning. Our method offers three key advantages: 1) efficient one-step noise-to-action generation, 2) expressive modelling of multimodal action distributions, and 3) efficient and stable policy learning via Q-learning in a single-stage training setup. Extensive experiments on 73 tasks across the OGBench and D4RL benchmarks demonstrate that our method achieves strong performance in both offline and offline-to-online reinforcement learning settings. Code is available at https://github.com/HiccupRL/MeanFlowQL.

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

The ability to learn multi-modal action distributions is indispensable for robotic manipulation policies to perform precise and robust control. Flow-based generative models have recently emerged as a promising solution to learning distributions of actions, offering one-step action generation and thus achieving much higher sampling efficiency compared to diffusion-based methods. However, existing flow-based policies suffer from representation collapse, the inability to distinguish similar visual representations, leading to failures in precise manipulation tasks. We propose DM1 (MeanFlow with Dispersive Regularization for One-Step Robotic Manipulation), a novel flow matching framework that integrates dispersive regularization into MeanFlow to prevent collapse while maintaining one-step efficiency. DM1 employs multiple dispersive regularization variants across different intermediate embedding layers, encouraging diverse representations across training batches without introducing additional network modules or specialized training procedures. Experiments on RoboMimic benchmarks show that DM1 achieves 20-40 times faster inference (0.07s vs. 2-3.5s) and improves success rates by 10-20 percentage points, with the Lift task reaching 99% success over 85% of the baseline. Real-robot deployment on a Franka Panda further validates that DM1 transfers effectively from simulation to the physical world. To the best of our knowledge, this is the first work to leverage representation regularization to enable flow-based policies to achieve strong performance in robotic manipulation, establishing a simple yet powerful approach for efficient and robust manipulation.

Recent advances in end-to-end autonomous driving leverage multi-view images to construct BEV representations for motion planning. In motion planning, autonomous vehicles need considering both hard constraints imposed by geometrically occupied obstacles (e.g., vehicles, pedestrians) and soft, rule-based semantics with no explicit geometry (e.g., lane boundaries, traffic priors). However, existing end-to-end frameworks typically rely on BEV features learned in an implicit manner, lacking explicit modeling of risk and guidance priors for safe and interpretable planning. To address this, we propose FlowDrive, a novel framework that introduces physically interpretable energy-based flow fields-including risk potential and lane attraction fields-to encode semantic priors and safety cues into the BEV space. These flow-aware features enable adaptive refinement of anchor trajectories and serve as interpretable guidance for trajectory generation. Moreover, FlowDrive decouples motion intent prediction from trajectory denoising via a conditional diffusion planner with feature-level gating, alleviating task interference and enhancing multimodal diversity. Experiments on the NAVSIM v2 benchmark demonstrate that FlowDrive achieves state-of-the-art performance with an EPDMS of 86.3, surpassing prior baselines in both safety and planning quality. The project is available at https://astrixdrive.github.io/FlowDrive.github.io/.

Flowcharts and mind maps, collectively known as flowmind, are vital in daily activities, with hand-drawn versions facilitating real-time collaboration. However, there's a growing need to digitize them for efficient processing. Automated conversion methods are essential to overcome manual conversion challenges. Existing sketch recognition methods face limitations in practical situations, being field-specific and lacking digital conversion steps. Our paper introduces the Flowmind2digital method and hdFlowmind dataset to address these challenges. Flowmind2digital, utilizing neural networks and keypoint detection, achieves a record 87.3% accuracy on our dataset, surpassing previous methods by 11.9%. The hdFlowmind dataset, comprising 1,776 annotated flowminds across 22 scenarios, outperforms existing datasets. Additionally, our experiments emphasize the importance of simple graphics, enhancing accuracy by 9.3%.

This monograph presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward process that gradually corrupts data into noise, linking the data distribution to a simple prior through a continuum of intermediate distributions. The goal is to learn a reverse process that transforms noise back into data while recovering the same intermediates. We describe three complementary views. The variational view, inspired by variational autoencoders, sees diffusion as learning to remove noise step by step. The score-based view, rooted in energy-based modeling, learns the gradient of the evolving data distribution, indicating how to nudge samples toward more likely regions. The flow-based view, related to normalizing flows, treats generation as following a smooth path that moves samples from noise to data under a learned velocity field. These perspectives share a common backbone: a time-dependent velocity field whose flow transports a simple prior to the data. Sampling then amounts to solving a differential equation that evolves noise into data along a continuous trajectory. On this foundation, the monograph discusses guidance for controllable generation, efficient numerical solvers, and diffusion-motivated flow-map models that learn direct mappings between arbitrary times. It provides a conceptual and mathematically grounded understanding of diffusion models for readers with basic deep-learning knowledge.

Flow maps enable high-quality image generation in a single forward pass. However, unlike iterative diffusion models, their lack of an explicit sampling trajectory impedes incorporating external constraints for conditional generation and solving inverse problems. We put forth Variational Flow Maps, a framework for conditional sampling that shifts the perspective of conditioning from "guiding a sampling path", to that of "learning the proper initial noise". Specifically, given an observation, we seek to learn a noise adapter model that outputs a noise distribution, so that after mapping to the data space via flow map, the samples respect the observation and data prior. To this end, we develop a principled variational objective that jointly trains the noise adapter and the flow map, improving noise-data alignment, such that sampling from complex data posterior is achieved with a simple adapter. Experiments on various inverse problems show that VFMs produce well-calibrated conditional samples in a single (or few) steps. For ImageNet, VFM attains competitive fidelity while accelerating the sampling by orders of magnitude compared to alternative iterative diffusion/flow models. Code is available at https://github.com/abbasmammadov/VFM

Group Relative Policy Optimization (GRPO) has shown strong potential for flow-matching-based text-to-image (T2I) generation, but it faces two key limitations: inaccurate advantage attribution, and the neglect of temporal dynamics of generation. In this work, we argue that shifting the optimization paradigm from the step level to the chunk level can effectively alleviate these issues. Building on this idea, we propose Chunk-GRPO, the first chunk-level GRPO-based approach for T2I generation. The insight is to group consecutive steps into coherent 'chunk's that capture the intrinsic temporal dynamics of flow matching, and to optimize policies at the chunk level. In addition, we introduce an optional weighted sampling strategy to further enhance performance. Extensive experiments show that ChunkGRPO achieves superior results in both preference alignment and image quality, highlighting the promise of chunk-level optimization for GRPO-based methods.

Modern conversational agents like ChatGPT and Alexa+ rely on predefined policies specifying metadata, response styles, and tool-usage rules. As these LLM-based systems expand to support diverse business and user queries, such policies, often implemented as in-context prompts, are becoming increasingly complex and lengthy, making faithful adherence difficult and imposing large fixed computational costs. With the rise of multimodal agents, policies that govern visual and multimodal behaviors are critical but remain understudied. Prior prompt-compression work mainly shortens task templates and demonstrations, while existing policy-alignment studies focus only on text-based safety rules. We introduce Multimodal Policy Internalization (MPI), a new task that internalizes reasoning-intensive multimodal policies into model parameters, enabling stronger policy-following without including the policy during inference. MPI poses unique data and algorithmic challenges. We build two datasets spanning synthetic and real-world decision-making and tool-using tasks and propose TriMPI, a three-stage training framework. TriMPI first injects policy knowledge via continual pretraining, then performs supervised finetuning, and finally applies PolicyRollout, a GRPO-style reinforcement learning extension that augments rollouts with policy-aware responses for grounded exploration. TriMPI achieves notable gains in end-to-end accuracy, generalization, and robustness to forgetting. As the first work on multimodal policy internalization, we provide datasets, training recipes, and comprehensive evaluations to foster future research. Project page: https://mikewangwzhl.github.io/TriMPI.

In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related state-action distribution--can be found all across the literature. Despite its importance, the state distribution is mostly discussed indirectly and theoretically, rather than being modeled explicitly. The reason being an absence of appropriate density estimation tools. In this work, we investigate applications of a normalizing flow-based model for the aforementioned distributions. In particular, we use a pair of flows coupled through the optimality point of the Donsker-Varadhan representation of the Kullback-Leibler (KL) divergence, for distribution matching based imitation learning. Our algorithm, Coupled Flow Imitation Learning (CFIL), achieves state-of-the-art performance on benchmark tasks with a single expert trajectory and extends naturally to a variety of other settings, including the subsampled and state-only regimes.

LLM-based agents have emerged as promising tools, which are crafted to fulfill complex tasks by iterative planning and action. However, these agents are susceptible to undesired planning hallucinations when lacking specific knowledge for expertise-intensive tasks. To address this, preliminary attempts are made to enhance planning reliability by incorporating external workflow-related knowledge. Despite the promise, such infused knowledge is mostly disorganized and diverse in formats, lacking rigorous formalization and comprehensive comparisons. Motivated by this, we formalize different formats of workflow knowledge and present FlowBench, the first benchmark for workflow-guided planning. FlowBench covers 51 different scenarios from 6 domains, with knowledge presented in diverse formats. To assess different LLMs on FlowBench, we design a multi-tiered evaluation framework. We evaluate the efficacy of workflow knowledge across multiple formats, and the results indicate that current LLM agents need considerable improvements for satisfactory planning. We hope that our challenging benchmark can pave the way for future agent planning research.

Why do pretrained diffusion or flow-matching policies fail when the same task is performed near an obstacle, on a shifted support surface, or amid mild clutter? Such failures rarely reflect missing motor skills; instead, they expose a limitation of imitation learning under train-test shifts, where action generation is tightly coupled to training-specific spatial configurations and task specifications. Retraining or fine-tuning to address these failures is costly and conceptually misaligned, as the required behaviors already exist but cannot be selectively adapted at test time. We propose Vision-Language Steering (VLS), a training-free framework for inference-time adaptation of frozen generative robot policies. VLS treats adaptation as an inference-time control problem, steering the sampling process of a pretrained diffusion or flow-matching policy in response to out-of-distribution observation-language inputs without modifying policy parameters. By leveraging vision-language models to synthesize trajectory-differentiable reward functions, VLS guides denoising toward action trajectories that satisfy test-time spatial and task requirements. Across simulation and real-world evaluations, VLS consistently outperforms prior steering methods, achieving a 31% improvement on CALVIN and a 13% gain on LIBERO-PRO. Real-world deployment on a Franka robot further demonstrates robust inference-time adaptation under test-time spatial and semantic shifts. Project page: https://vision-language-steering.github.io/webpage/

Aligning streaming autoregressive (AR) video generators with human preferences is challenging. Existing reinforcement learning methods predominantly rely on noise-based exploration and SDE-based surrogate policies that are mismatched to the deterministic ODE dynamics of distilled AR models, and tend to perturb low-level appearance rather than the high-level semantic storyline progression critical for long-horizon coherence. To address these limitations, we present KVPO, an ODE-native online Group Relative Policy Optimization (GRPO) framework for aligning streaming video generators. For diversity exploration, KVPO introduces a causal-semantic exploration paradigm that relocates the source of variation from stochastic noise to the historical KV cache. By stochastically routing historical KV entries, it constructs semantically diverse generation branches that remain strictly on the data manifold. For policy modeling, KVPO introduces a velocity-field surrogate policy based on Trajectory Velocity Energy (TVE), which quantifies branch likelihood in flow-matching velocity space and yields a reward-weighted contrastive objective fully consistent with the native ODE formulation. Experiments on multiple distilled AR video generators demonstrate consistent gains in visual quality, motion quality, and text-video alignment across both single-prompt short-video and multi-prompt long-video settings.

Generative flow networks (GFlowNets) are a method for learning a stochastic policy for generating compositional objects, such as graphs or strings, from a given unnormalized density by sequences of actions, where many possible action sequences may lead to the same object. We find previously proposed learning objectives for GFlowNets, flow matching and detailed balance, which are analogous to temporal difference learning, to be prone to inefficient credit propagation across long action sequences. We thus propose a new learning objective for GFlowNets, trajectory balance, as a more efficient alternative to previously used objectives. We prove that any global minimizer of the trajectory balance objective can define a policy that samples exactly from the target distribution. In experiments on four distinct domains, we empirically demonstrate the benefits of the trajectory balance objective for GFlowNet convergence, diversity of generated samples, and robustness to long action sequences and large action spaces.

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

We propose Flow-GRPO, the first method integrating online reinforcement learning (RL) into flow matching models. Our approach uses two key strategies: (1) an ODE-to-SDE conversion that transforms a deterministic Ordinary Differential Equation (ODE) into an equivalent Stochastic Differential Equation (SDE) that matches the original model's marginal distribution at all timesteps, enabling statistical sampling for RL exploration; and (2) a Denoising Reduction strategy that reduces training denoising steps while retaining the original inference timestep number, significantly improving sampling efficiency without performance degradation. Empirically, Flow-GRPO is effective across multiple text-to-image tasks. For complex compositions, RL-tuned SD3.5 generates nearly perfect object counts, spatial relations, and fine-grained attributes, boosting GenEval accuracy from 63% to 95%. In visual text rendering, its accuracy improves from 59% to 92%, significantly enhancing text generation. Flow-GRPO also achieves substantial gains in human preference alignment. Notably, little to no reward hacking occurred, meaning rewards did not increase at the cost of image quality or diversity, and both remained stable in our experiments.

Recent flow matching models for text-to-image generation have achieved remarkable quality, yet their integration with reinforcement learning for human preference alignment remains suboptimal, hindering fine-grained reward-based optimization. We observe that the key impediment to effective GRPO training of flow models is the temporal uniformity assumption in existing approaches: sparse terminal rewards with uniform credit assignment fail to capture the varying criticality of decisions across generation timesteps, resulting in inefficient exploration and suboptimal convergence. To remedy this shortcoming, we introduce TempFlow-GRPO (Temporal Flow GRPO), a principled GRPO framework that captures and exploits the temporal structure inherent in flow-based generation. TempFlow-GRPO introduces two key innovations: (i) a trajectory branching mechanism that provides process rewards by concentrating stochasticity at designated branching points, enabling precise credit assignment without requiring specialized intermediate reward models; and (ii) a noise-aware weighting scheme that modulates policy optimization according to the intrinsic exploration potential of each timestep, prioritizing learning during high-impact early stages while ensuring stable refinement in later phases. These innovations endow the model with temporally-aware optimization that respects the underlying generative dynamics, leading to state-of-the-art performance in human preference alignment and standard text-to-image benchmarks.

We propose GoalFlow, an end-to-end autonomous driving method for generating high-quality multimodal trajectories. In autonomous driving scenarios, there is rarely a single suitable trajectory. Recent methods have increasingly focused on modeling multimodal trajectory distributions. However, they suffer from trajectory selection complexity and reduced trajectory quality due to high trajectory divergence and inconsistencies between guidance and scene information. To address these issues, we introduce GoalFlow, a novel method that effectively constrains the generative process to produce high-quality, multimodal trajectories. To resolve the trajectory divergence problem inherent in diffusion-based methods, GoalFlow constrains the generated trajectories by introducing a goal point. GoalFlow establishes a novel scoring mechanism that selects the most appropriate goal point from the candidate points based on scene information. Furthermore, GoalFlow employs an efficient generative method, Flow Matching, to generate multimodal trajectories, and incorporates a refined scoring mechanism to select the optimal trajectory from the candidates. Our experimental results, validated on the NavsimDauner2024_navsim, demonstrate that GoalFlow achieves state-of-the-art performance, delivering robust multimodal trajectories for autonomous driving. GoalFlow achieved PDMS of 90.3, significantly surpassing other methods. Compared with other diffusion-policy-based methods, our approach requires only a single denoising step to obtain excellent performance. The code is available at https://github.com/YvanYin/GoalFlow.

As trajectories sampled by policies used by reinforcement learning (RL) and generative flow networks (GFlowNets) grow longer, credit assignment and exploration become more challenging, and the long planning horizon hinders mode discovery and generalization. The challenge is particularly pronounced in entropy-seeking RL methods, such as generative flow networks, where the agent must learn to sample from a structured distribution and discover multiple high-reward states, each of which take many steps to reach. To tackle this challenge, we propose an approach to incorporate the discovery of action abstractions, or high-level actions, into the policy optimization process. Our approach involves iteratively extracting action subsequences commonly used across many high-reward trajectories and `chunking' them into a single action that is added to the action space. In empirical evaluation on synthetic and real-world environments, our approach demonstrates improved sample efficiency performance in discovering diverse high-reward objects, especially on harder exploration problems. We also observe that the abstracted high-order actions are interpretable, capturing the latent structure of the reward landscape of the action space. This work provides a cognitively motivated approach to action abstraction in RL and is the first demonstration of hierarchical planning in amortized sequential sampling.

Editing real images using a pre-trained text-to-image (T2I) diffusion/flow model often involves inverting the image into its corresponding noise map. However, inversion by itself is typically insufficient for obtaining satisfactory results, and therefore many methods additionally intervene in the sampling process. Such methods achieve improved results but are not seamlessly transferable between model architectures. Here, we introduce FlowEdit, a text-based editing method for pre-trained T2I flow models, which is inversion-free, optimization-free and model agnostic. Our method constructs an ODE that directly maps between the source and target distributions (corresponding to the source and target text prompts) and achieves a lower transport cost than the inversion approach. This leads to state-of-the-art results, as we illustrate with Stable Diffusion 3 and FLUX. Code and examples are available on the project's webpage.

Diffusion and flow models have become the dominant paradigm for generative modeling on Riemannian manifolds, with successful applications in protein backbone generation and DNA sequence design. However, these methods require tens to hundreds of neural network evaluations at inference time, which can become a computational bottleneck in large-scale scientific sampling workflows. We introduce Riemannian MeanFlow~(RMF), a framework for learning flow maps directly on manifolds, enabling high-quality generations with as few as one forward pass. We derive three equivalent characterizations of the manifold average velocity (Eulerian, Lagrangian, and semigroup identities), and analyze parameterizations and stabilization techniques to improve training on high-dimensional manifolds. In promoter DNA design and protein backbone generation settings, RMF achieves comparable sample quality to prior methods while requiring up to 10times fewer function evaluations. Finally, we show that few-step flow maps enable efficient reward-guided design through reward look-ahead, where terminal states can be predicted from intermediate steps at minimal additional cost.

Combinatorial optimization (CO) problems are often NP-hard and thus out of reach for exact algorithms, making them a tempting domain to apply machine learning methods. The highly structured constraints in these problems can hinder either optimization or sampling directly in the solution space. On the other hand, GFlowNets have recently emerged as a powerful machinery to efficiently sample from composite unnormalized densities sequentially and have the potential to amortize such solution-searching processes in CO, as well as generate diverse solution candidates. In this paper, we design Markov decision processes (MDPs) for different combinatorial problems and propose to train conditional GFlowNets to sample from the solution space. Efficient training techniques are also developed to benefit long-range credit assignment. Through extensive experiments on a variety of different CO tasks with synthetic and realistic data, we demonstrate that GFlowNet policies can efficiently find high-quality solutions.

State-of-the-art flow models achieve remarkable quality but require slow, iterative sampling. To accelerate this, flow maps can be distilled from pre-trained teachers, a procedure that conventionally requires sampling from an external dataset. We argue that this data-dependency introduces a fundamental risk of Teacher-Data Mismatch, as a static dataset may provide an incomplete or even misaligned representation of the teacher's full generative capabilities. This leads us to question whether this reliance on data is truly necessary for successful flow map distillation. In this work, we explore a data-free alternative that samples only from the prior distribution, a distribution the teacher is guaranteed to follow by construction, thereby circumventing the mismatch risk entirely. To demonstrate the practical viability of this philosophy, we introduce a principled framework that learns to predict the teacher's sampling path while actively correcting for its own compounding errors to ensure high fidelity. Our approach surpasses all data-based counterparts and establishes a new state-of-the-art by a significant margin. Specifically, distilling from SiT-XL/2+REPA, our method reaches an impressive FID of 1.45 on ImageNet 256x256, and 1.49 on ImageNet 512x512, both with only 1 sampling step. We hope our work establishes a more robust paradigm for accelerating generative models and motivates the broader adoption of flow map distillation without data.

Generative control policies (GCPs), such as diffusion- and flow-based control policies, have emerged as effective parameterizations for robot learning. This work introduces Off-policy Generative Policy Optimization (OGPO), a sample-efficient algorithm for finetuning GCPs that maintains off-policy critic networks to maximize data reuse and propagate policy gradients through the full generative process of the policy via a modified PPO objective, using critics as the terminal reward. OGPO achieves state-of-the-art performance on manipulation tasks spanning multi-task settings, high-precision insertion, and dexterous control. To our knowledge, it is also the only method that can fine-tune poorly-initialized behavior cloning policies to near full task-success with no expert data in the online replay buffer, and does so with few task-specific hyperparameter tuning. Through extensive empirical investigations, we demonstrate that OGPO drastically outperforms methods alternatives on policy steering and learning residual corrections, and identify the key mechanisms behind its performance. We further introduce practical stabilization tricks, including success-buffer regularization, two-sided conservative advantages, and Q-variance reduction, to mitigate critic over-exploitation across state- and pixel-based settings. Beyond proposing OGPO, we conduct a systematic empirical study of GCP finetuning, identifying the stabilizing mechanisms and failure modes that govern successful off-policy full-policy improvement.

Reinforcement learning (RL) faces a persistent tension: policies that are stable to optimize are often too simple to represent the multimodal action distributions needed for complex control. Gaussian policies provide tractable likelihoods and smooth gradients, but their unimodal form limits expressiveness. Conversely, generative policies based on diffusion or flow matching can model rich multimodal behaviors; however, in online RL, they are frequently unstable due to intractable likelihoods and noisy gradients propagating through deep sampling chains. We address this tension with a key structural principle: decoupling optimization from generation. Building on this insight, we introduce GoRL (Generative Online Reinforcement Learning), a framework that optimizes a tractable latent policy while utilizing a conditional generative decoder to synthesize actions. A two-timescale update schedule enables the latent policy to learn stably while the decoder steadily increases expressiveness, without requiring tractable action likelihoods. Across a range of continuous-control tasks, GoRL consistently outperforms both Gaussian policies and recent generative-policy baselines. Notably, on the HopperStand task, it reaches a normalized return above 870, more than 3 times that of the strongest baseline. These results demonstrate that separating optimization from generation provides a practical path to policies that are both stable and highly expressive.

We present Piecewise Rectified Flow (PeRFlow), a flow-based method for accelerating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piecewise linear flows. PeRFlow achieves superior performance in a few-step generation. Moreover, through dedicated parameterizations, the obtained PeRFlow models show advantageous transfer ability, serving as universal plug-and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models. The implementations of training and inference are fully open-sourced. https://github.com/magic-research/piecewise-rectified-flow

Modern image generation demands a single model that unifies diverse capabilities, including text-to-image (T2I), local editing, and global editing. However, these capabilities are rarely naturally aligned and often conflict. For instance, editing tends to degrade T2I performance, while global and local editing interfere with each other. Consequently, effectively composing these capabilities has become a central challenge for image generation model training. To tackle this, we introduce DanceOPD, an on-policy generative field distillation framework for flow-matching models that routes each sample to one capability field, queries one low-noise student-induced state, and trains with a simple velocity MSE objective. With each capability source defined as a velocity field over the shared flow state space, the student learns from fields queried on its own rollout states to compose expert capabilities. This formulation also absorbs operator-defined fields such as classifier-free guidance. Comprehensive experiments on T2I, editing, realism-field absorption, and CFG absorption show that our approach improves multi-capability composition, strengthening target capabilities while preserving anchor generation quality. We believe this work establishes a practical route for generative field distillation in flow-matching models.

Generative flow networks (GFlowNets) are a family of algorithms that learn a generative policy to sample discrete objects x with non-negative reward R(x). Learning objectives guarantee the GFlowNet samples x from the target distribution p^*(x) propto R(x) when loss is globally minimized over all states or trajectories, but it is unclear how well they perform with practical limits on training resources. We introduce an efficient evaluation strategy to compare the learned sampling distribution to the target reward distribution. As flows can be underdetermined given training data, we clarify the importance of learned flows to generalization and matching p^*(x) in practice. We investigate how to learn better flows, and propose (i) prioritized replay training of high-reward x, (ii) relative edge flow policy parametrization, and (iii) a novel guided trajectory balance objective, and show how it can solve a substructure credit assignment problem. We substantially improve sample efficiency on biochemical design tasks.

The rapidly evolving field of Robotic Process Automation (RPA) has made significant strides in automating repetitive processes, yet its effectiveness diminishes in scenarios requiring spontaneous or unpredictable tasks demanded by users. This paper introduces a novel approach, FlowMind, leveraging the capabilities of Large Language Models (LLMs) such as Generative Pretrained Transformer (GPT), to address this limitation and create an automatic workflow generation system. In FlowMind, we propose a generic prompt recipe for a lecture that helps ground LLM reasoning with reliable Application Programming Interfaces (APIs). With this, FlowMind not only mitigates the common issue of hallucinations in LLMs, but also eliminates direct interaction between LLMs and proprietary data or code, thus ensuring the integrity and confidentiality of information - a cornerstone in financial services. FlowMind further simplifies user interaction by presenting high-level descriptions of auto-generated workflows, enabling users to inspect and provide feedback effectively. We also introduce NCEN-QA, a new dataset in finance for benchmarking question-answering tasks from N-CEN reports on funds. We used NCEN-QA to evaluate the performance of workflows generated by FlowMind against baseline and ablation variants of FlowMind. We demonstrate the success of FlowMind, the importance of each component in the proposed lecture recipe, and the effectiveness of user interaction and feedback in FlowMind.

We propose a unified, few-step generative modeling framework based on cumulative flow maps for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a cumulative-flow abstraction that connects local, instantaneous updates with finite-time transport, enabling generative models to reason about global state transitions. This perspective yields a unified few-step framework built on cumulative transport and cumulative parameterization that applies broadly to existing diffusion- and flow-based models without being tied to a specific prediction instantiation. Our formulation supports few-step and even one-step generation while preserving synthesis quality, requiring only minimal changes to time embeddings and training objectives, and no increase in model capacity. We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation, with reduced inference cost.

Recent progress in flow-based generative models and reinforcement learning (RL) has improved text-image alignment and visual quality. However, current RL training for flow models still has two main problems: (i) GRPO-style fixed per-prompt group sizes ignore variation in sampling importance across prompts, which leads to inefficient sampling and slower training; and (ii) trajectory-level advantages are reused as per-step estimates, which biases credit assignment along the flow. We propose SuperFlow, an RL training framework for flow-based models that adjusts group sizes with variance-aware sampling and computes step-level advantages in a way that is consistent with continuous-time flow dynamics. Empirically, SuperFlow reaches promising performance while using only 5.4% to 56.3% of the original training steps and reduces training time by 5.2% to 16.7% without any architectural changes. On standard text-to-image (T2I) tasks, including text rendering, compositional image generation, and human preference alignment, SuperFlow improves over SD3.5-M by 4.6% to 47.2%, and over Flow-GRPO by 1.7% to 16.0%.

Real-time robotic control demands fast action generation. However, existing generative policies based on diffusion and flow matching require multi-step sampling, fundamentally limiting deployment in time-critical scenarios. We propose Dispersive MeanFlow Policy Optimization (DMPO), a unified framework that enables true one-step generation through three key components: MeanFlow for mathematically-derived single-step inference without knowledge distillation, dispersive regularization to prevent representation collapse, and reinforcement learning (RL) fine-tuning to surpass expert demonstrations. Experiments across RoboMimic manipulation and OpenAI Gym locomotion benchmarks demonstrate competitive or superior performance compared to multi-step baselines. With our lightweight model architecture and the three key algorithmic components working in synergy, DMPO exceeds real-time control requirements (>120Hz) with 5-20x inference speedup, reaching hundreds of Hertz on high-performance GPUs. Physical deployment on a Franka-Emika-Panda robot validates real-world applicability.

Iterative generative policies, such as diffusion models and flow matching, offer superior expressivity for continuous control but complicate Maximum Entropy Reinforcement Learning because their action log-densities are not directly accessible. To address this, we propose Field Least-Energy Actor-Critic (FLAC), a likelihood-free framework that regulates policy stochasticity by penalizing the kinetic energy of the velocity field. Our key insight is to formulate policy optimization as a Generalized Schrödinger Bridge (GSB) problem relative to a high-entropy reference process (e.g., uniform). Under this view, the maximum-entropy principle emerges naturally as staying close to a high-entropy reference while optimizing return, without requiring explicit action densities. In this framework, kinetic energy serves as a physically grounded proxy for divergence from the reference: minimizing path-space energy bounds the deviation of the induced terminal action distribution. Building on this view, we derive an energy-regularized policy iteration scheme and a practical off-policy algorithm that automatically tunes the kinetic energy via a Lagrangian dual mechanism. Empirically, FLAC achieves superior or comparable performance on high-dimensional benchmarks relative to strong baselines, while avoiding explicit density estimation.

We develop a novel policy synthesis algorithm, RMPflow, based on geometrically consistent transformations of Riemannian Motion Policies (RMPs). RMPs are a class of reactive motion policies designed to parameterize non-Euclidean behaviors as dynamical systems in intrinsically nonlinear task spaces. Given a set of RMPs designed for individual tasks, RMPflow can consistently combine these local policies to generate an expressive global policy, while simultaneously exploiting sparse structure for computational efficiency. We study the geometric properties of RMPflow and provide sufficient conditions for stability. Finally, we experimentally demonstrate that accounting for the geometry of task policies can simplify classically difficult problems, such as planning through clutter on high-DOF manipulation systems.

Generative Flow Networks (GFlowNets) are amortized sampling methods that learn a distribution over discrete objects proportional to their rewards. GFlowNets exhibit a remarkable ability to generate diverse samples, yet occasionally struggle to consistently produce samples with high rewards due to over-exploration on wide sample space. This paper proposes to train GFlowNets with local search, which focuses on exploiting high-rewarded sample space to resolve this issue. Our main idea is to explore the local neighborhood via backtracking and reconstruction guided by backward and forward policies, respectively. This allows biasing the samples toward high-reward solutions, which is not possible for a typical GFlowNet solution generation scheme, which uses the forward policy to generate the solution from scratch. Extensive experiments demonstrate a remarkable performance improvement in several biochemical tasks. Source code is available: https://github.com/dbsxodud-11/ls_gfn.

While online Reinforcement Learning has emerged as a crucial technique for aligning flow matching models with human preferences, current approaches are hindered by inefficient exploration during training rollouts. Relying on undirected stochasticity and sparse outcome rewards, these methods struggle to discover high-reward samples, resulting in data-inefficient and slow optimization. To address these limitations, we propose Euphonium, a novel framework that steers generation via process reward gradient guided dynamics. Our key insight is to formulate the sampling process as a theoretically principled Stochastic Differential Equation that explicitly incorporates the gradient of a Process Reward Model into the flow drift. This design enables dense, step-by-step steering toward high-reward regions, advancing beyond the unguided exploration in prior works, and theoretically encompasses existing sampling methods (e.g., Flow-GRPO, DanceGRPO) as special cases. We further derive a distillation objective that internalizes the guidance signal into the flow network, eliminating inference-time dependency on the reward model. We instantiate this framework with a Dual-Reward Group Relative Policy Optimization algorithm, combining latent process rewards for efficient credit assignment with pixel-level outcome rewards for final visual fidelity. Experiments on text-to-video generation show that Euphonium achieves better alignment compared to existing methods while accelerating training convergence by 1.66x.

Expressive generative policies such as diffusion and flow models are appealing for MaxEnt online reinforcement learning because of their ability to model multimodal and highly non-Gaussian action distributions. However, training effective soft generative policies faces two obstacles that often arise together. First, marginal action densities are often unavailable, so existing methods typically rely on entropy bounds, heuristic proxies or approximations. Second, iterative shared-parameter samplers raise inference cost and require backpropagation through time over repeated network evaluations, increasing memory cost and destabilizing policy optimization. These obstacles motivate us to seek a generative policy that exposes a tractable MaxEnt objective while requiring only a single sampled actor forward pass for action generation. To this end, we propose soft generative actor-critic (SoftGAC), whose actor defines a stochastic bridge from a fixed base latent to a terminal action latent in pre-tanh space. This structured bridge allows us to lift the MaxEnt objective as an analytically tractable path-wise relative-entropy objective against a high-entropy reference process. In practical finite-step implementation, this relative entropy reduces exactly to sampled transition control energy and thus provides principled soft regularization. Moreover, we keep the single-pass actor lightweight by using small step-specific bridge transitions, each evaluated only once per sampled action, while maintaining a parameter budget comparable to strong actor baselines. Extensive experiments on challenging continuous-control benchmarks show that SoftGAC attains higher or competitive returns than strong generative policy baselines, including diffusion and flow-matching policies, while staying in the low-latency regime of one-pass actors and showing considerable improvements in the compute-return tradeoff.

Reinforcement Learning (RL) has recently emerged as a powerful technique for improving image and video generation in Diffusion and Flow Matching models, specifically for enhancing output quality and alignment with prompts. A critical step for applying online RL methods on Flow Matching is the introduction of stochasticity into the deterministic framework, commonly realized by Stochastic Differential Equation (SDE). Our investigation reveals a significant drawback to this approach: SDE-based sampling introduces pronounced noise artifacts in the generated images, which we found to be detrimental to the reward learning process. A rigorous theoretical analysis traces the origin of this noise to an excess of stochasticity injected during inference. To address this, we draw inspiration from Denoising Diffusion Implicit Models (DDIM) to reformulate the sampling process. Our proposed method, Coefficients-Preserving Sampling (CPS), eliminates these noise artifacts. This leads to more accurate reward modeling, ultimately enabling faster and more stable convergence for reinforcement learning-based optimizers like Flow-GRPO and Dance-GRPO. Code will be released at https://github.com/IamCreateAI/FlowCPS