# Refinement-based Flow Policy Optimization

arXiv: https://arxiv.org/abs/2609.15123 · HTML: https://mlsanity.com/paper/2609.15123/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Deep reinforcement learning methods / [RL with diffusion and flow models](https://mlsanity.com/deeprl/rl-with-diffusion-and-flow-models/)

## Builds on (most cited first, 18 of 18)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Learning a Diffusion Model Policy from Rewards via Q-Score Matching](https://mlsanity.com/paper/2312.11752/) (2023)
- [Policy Representation via Diffusion Probability Model for Reinforcement Learning](https://mlsanity.com/paper/2305.13122/) (2023)
- [Diffusion-based Reinforcement Learning via Q-weighted Variational Policy Optimization](https://mlsanity.com/paper/2405.16173/) (2024)
- [Diffusion Actor-Critic with Entropy Regulator](https://mlsanity.com/paper/2405.15177/) (2024)
- [Efficient Online Reinforcement Learning for Diffusion Policy](https://mlsanity.com/paper/2502.00361/) (2025)
- [Learning to Draw Samples with Amortized Stein Variational Gradient Descent](https://mlsanity.com/paper/1707.06626/) (2017)
- [Approximate Inference with Amortised MCMC](https://mlsanity.com/paper/1702.08343/) (2017)
- [Optimal Preconditioning and Fisher Adaptive Langevin Sampling](https://mlsanity.com/paper/2305.14442/) (2023)
- [Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policies](https://mlsanity.com/paper/2601.08136/) (2026)
- [Real-Time Generative Policy via Langevin-Guided Flow Matching for Autonomous Driving](https://mlsanity.com/paper/2603.02613/) (2026)

## Abstract (arXiv)

Flow-based policies offer an expressive representation for online reinforcement learning, but conventional flow matching requires samples drawn from the distribution to be modeled. This poses a challenge when the desired action distribution is defined only implicitly by a Q-function, since directly sampling actions from the resulting distribution is generally intractable. We propose Refinement-Based Flow Policy Optimization (RFPO), a novel framework for training a flow policy in online reinforcement learning by alternating between Q-guided sample refinement and self-target flow matching. RFPO first generates actions from Gaussian noise using the current flow policy and then uses a finite-step stochastic refinement procedure to move them toward an energy-based distribution induced by the Q-function. Each refined action is then paired with its corresponding initial noise sample and used as a fixed target for flow-matching training. By repeatedly refining its own outputs and learning from the resulting targets, RFPO incorporates Q-guidance into the policy without requiring direct samples from the target distribution, while retaining the capacity to represent multiple action modes. We further provide a theoretical analysis of the distributional dynamics induced by RFPO. Across six continuous-control tasks, RFPO matches or outperforms a standard Gaussian-policy baseline on almost every task. Experiments on six synthetic two-dimensional target distributions with diverse geometries demonstrate that RFPO captures complex multimodal structure without mode collapse.