# ReFPO: Reflow Regularization for Flow Matching Policy Gradients

arXiv: https://arxiv.org/abs/2606.21086 · HTML: https://mlsanity.com/paper/2606.21086/

## 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 42 of its 47 references that are in the map.
- First posted on arXiv 19 Jun 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, 30 of 42)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [dm_control: Software and Tasks for Continuous Control](https://mlsanity.com/paper/2006.12983/) (2020)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [Perpetual Humanoid Control for Real-time Simulated Avatars](https://mlsanity.com/paper/2305.06456/) (2023)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [MixGRPO: Unlocking Flow-based GRPO Efficiency with Mixed ODE-SDE](https://mlsanity.com/paper/2507.21802/) (2025)
- [Reinforcement Learning with Action Chunking](https://mlsanity.com/paper/2507.07969/) (2025)
- [Consistency Flow Matching: Defining Straight Flows with Velocity Consistency](https://mlsanity.com/paper/2407.02398/) (2024)
- [Flow Matching Policy Gradients](https://mlsanity.com/paper/2507.21053/) (2025)
- [ReinFlow: Fine-tuning Flow Matching Policy with Online Reinforcement Learning](https://mlsanity.com/paper/2505.22094/) (2025)
- [Optimal Flow Matching: Learning Straight Trajectories in Just One Step](https://mlsanity.com/paper/2403.13117/) (2024)
- [Energy-Weighted Flow Matching for Offline Reinforcement Learning](https://mlsanity.com/paper/2503.04975/) (2025)
- [FastTD3: Simple, Fast, and Capable Reinforcement Learning for Humanoid Control](https://mlsanity.com/paper/2505.22642/) (2025)
- [Online Reward-Weighted Fine-Tuning of Flow Matching with Wasserstein Regularization](https://mlsanity.com/paper/2502.06061/) (2025)

## Abstract (arXiv)

We present Reflow-regularized Flow Matching Policy Gradients (ReFPO), a simple online RL method that adds explicit Reflow regularization to FPO for efficient flow-based control. We uncover a key structural property: the gradient updates in Flow Matching Policy Gradients (FPO) can be interpreted as an implicit advantage-weighted Reflow process, providing a new geometric perspective on flow-based policy gradients. Building on this insight, ReFPO introduces an explicit geometric regularizer that can be implemented with a single line of code change without incurring additional computational overhead or auxiliary distillation stages. By synergizing advantage-guided updates with path rectification, our method reduces CFM proxy-ratio spikes, stabilizes PPO-style training, and enables high-fidelity one-step inference that often matches or exceeds multi-step performance. We experimentally demonstrate that ReFPO improves average performance and discretization robustness across GridWorld, MuJoCo Playground, and high-dimensional Humanoid Control tasks, providing a scalable and stable approach for generative policies in complex physical simulations.