We propose Q-learning with Adjoint Matching (QAM), a novel TD-based reinforcement learning (RL) algorithm that tackles a long-standing challenge in continuous-action RL: efficient optimization of an expressive diffusion or flow-matching policy with respect to a parameterized Q-function. Effective optimization requires exploiting the first-order information of the critic, but it is challenging to do so for flow or diffusion policies because direct gradient-based optimization via backpropagation through their multi-step denoising process is numerically unstable. Existing methods work around this either by only using the value and discarding the gradient information, or by relying on approximations that sacrifice policy expressivity or bias the learned policy. QAM sidesteps both of these challenges by leveraging adjoint matching, a recently proposed technique in generative modeling, which transforms the critic's action gradient to form a step-wise objective function that is free from unstable backpropagation, while providing an unbiased, expressive policy at the optimum. Combined with temporal-difference backup for critic learning, QAM consistently outperforms prior approaches on hard, sparse reward tasks in both offline and offline-to-online RL.

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/

While behavior cloning with flow/diffusion policies excels at learning complex skills from demonstrations, it remains vulnerable to distributional shift, and standard RL methods struggle to fine-tune these models due to their iterative inference process and the limitations of existing workarounds. In this work, we introduce the Stepwise Flow Policy (SWFP) framework, founded on the key insight that discretizing the flow matching inference process via a fixed-step Euler scheme inherently aligns it with the variational Jordan-Kinderlehrer-Otto (JKO) principle from optimal transport. SWFP decomposes the global flow into a sequence of small, incremental transformations between proximate distributions. Each step corresponds to a JKO update, regularizing policy changes to stay near the previous iterate and ensuring stable online adaptation with entropic regularization. This decomposition yields an efficient algorithm that fine-tunes pre-trained flows via a cascade of small flow blocks, offering significant advantages: simpler/faster training of sub-models, reduced computational/memory costs, and provable stability grounded in Wasserstein trust regions. Comprehensive experiments demonstrate SWFP's enhanced stability, efficiency, and superior adaptation performance across diverse robotic control benchmarks.

Diffusion policies have achieved great success in online reinforcement learning (RL) due to their strong expressive capacity. However, the inference of diffusion policy models relies on a slow iterative sampling process, which limits their responsiveness. To overcome this limitation, we propose Flow Policy Mirror Descent (FPMD), an online RL algorithm that enables 1-step sampling during flow policy inference. Our approach exploits a theoretical connection between the distribution variance and the discretization error of single-step sampling in straight interpolation flow matching models, and requires no extra distillation or consistency training. We present two algorithm variants based on rectified flow policy and MeanFlow policy, respectively. Extensive empirical evaluations on MuJoCo and visual DeepMind Control Suite benchmarks demonstrate that our algorithms show strong performance comparable to diffusion policy baselines while requiring orders of magnitude less computational cost during inference. Diffusion models have established themselves as the state-of-the-art paradigm in generative modeling (Ho et al., 2020; Dhariwal & Nichol, 2021), capable of synthesizing data of unparalleled quality and diversity across various modalities, including images, audio, and video. The success is rooted in a principled, thermodynamically-inspired framework that learns to reverse a gradual noising process (Sohl-Dickstein et al., 2015).

Centralized trajectory optimization in the joint space of multiple robots allows access to a larger feasible space that can result in smoother trajectories, especially while planning in tight spaces. Unfortunately, it is often computationally intractable beyond a very small swarm size. In this paper, we propose Flow-Opt, a learning-based approach towards improving the computational tractability of centralized multi-robot trajectory optimization. Specifically, we reduce the problem to first learning a generative model to sample different candidate trajectories and then using a learned Safety-Filter(SF) to ensure fast inference-time constraint satisfaction. We propose a flow-matching model with a diffusion transformer (DiT) augmented with permutation invariant robot position and map encoders as the generative model. We develop a custom solver for our SF and equip it with a neural network that predicts context-specific initialization. The initialization network is trained in a self-supervised manner, taking advantage of the differentiability of the SF solver. We advance the state-of-the-art in the following respects. First, we show that we can generate trajectories of tens of robots in cluttered environments in a few tens of milliseconds. This is several times faster than existing centralized optimization approaches. Moreover, our approach also generates smoother trajectories orders of magnitude faster than competing baselines based on diffusion models. Second, each component of our approach can be batched, allowing us to solve a few tens of problem instances in a fraction of a second. We believe this is a first such result; no existing approach provides such capabilities. Finally, our approach can generate a diverse set of trajectories between a given set of start and goal locations, which can capture different collision-avoidance behaviors.

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/

In recent years, generative models have shown remarkable capabilities across diverse fields, including images, videos, language, and decision-making. By applying powerful generative models such as flow-based models to reinforcement learning, we can effectively model complex multi-modal action distributions and achieve superior robotic control in continuous action spaces, surpassing the limitations of single-modal action distributions with traditional Gaussian-based policies. Previous methods usually adopt the generative models as behavior models to fit state-conditioned action distributions from datasets, with policy optimization conducted separately through additional policies using value-based sample weighting or gradient-based updates. However, this separation prevents the simultaneous optimization of multi-modal distribution fitting and policy improvement, ultimately hindering the training of models and degrading the performance. To address this issue, we propose Decision Flow, a unified framework that integrates multi-modal action distribution modeling and policy optimization. Specifically, our method formulates the action generation procedure of flow-based models as a flow decision-making process, where each action generation step corresponds to one flow decision. Consequently, our method seamlessly optimizes the flow policy while capturing multi-modal action distributions. We provide rigorous proofs of Decision Flow and validate the effectiveness through extensive experiments across dozens of offline RL environments. Compared with established offline RL baselines, the results demonstrate that our method achieves or matches the SOTA performance.

However, leveraging flow or diffusion models to parameterize Offline reinforcement learning (RL) enables training an effective policies for offline RL is not a trivial problem. Unlike decision-making policy from a previously collected with simpler policy classes, such as Gaussian policies, there dataset without costly environment interactions (Lange et al., is no straightforward way to train the flow or diffusion policies 2012; Levine et al., 2020). The essence of offline RL to maximize a learned value function, due to the iterative is constrained optimization: the agent must maximize returns nature of these generative models. This is an example while staying within the dataset's state-action distribution of a policy extraction problem, which is known to be a key (Levine et al., 2020). As datasets have grown larger and challenge in offline RL in general (Park et al., 2024a). Previous more diverse (Collaboration et al., 2024), their behavioral works have devised diverse ways to extract an iterative distributions have become more complex and multimodal, generative policy from a learned value function, based and this often necessitates an expressive policy class (Mandlekar on weighted regression, reparameterized policy gradient, rejection et al., 2021) capable of capturing these complex distributions sampling, and other techniques. While they have and implementing a more precise behavioral constraint.