# Score-Based One-step MeanFlow Policy Optimization

arXiv: https://arxiv.org/abs/2605.23365 · HTML: https://mlsanity.com/paper/2605.23365/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 28 of its 32 references that are in the map.
- First posted on arXiv 22 May 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, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [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)
- [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)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [Learning a Diffusion Model Policy from Rewards via Q-Score Matching](https://mlsanity.com/paper/2312.11752/) (2023)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [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)
- [Score Regularized Policy Optimization through Diffusion Behavior](https://mlsanity.com/paper/2310.07297/) (2023)
- [Efficient Online Reinforcement Learning for Diffusion Policy](https://mlsanity.com/paper/2502.00361/) (2025)
- [Prior-Guided Diffusion Planning for Offline Reinforcement Learning](https://mlsanity.com/paper/2505.10881/) (2025)
- [Mean Flow Policy with Instantaneous Velocity Constraint for One-step Action Generation](https://mlsanity.com/paper/2602.13810/) (2026)

## Built on by (most cited first, 2 of 2)

- [Expressivity and Statistical Trade-offs in Diffusion Policy Learning](https://mlsanity.com/paper/2607.07967/) (2026)
- [Drift, Then Spread: Learning One-Step Generative Policies for Online Reinforcement Learning](https://mlsanity.com/paper/2610.15662/) (2026)

## Abstract (arXiv)

Diffusion and flow matching have emerged as expressive policy classes in reinforcement learning, but their reliance on multi-step denoising imposes substantial computational overhead at inference time, which is particularly problematic in online RL. MeanFlow offers a promising alternative by learning an average velocity field that maps noise to data in a single network evaluation. However, MeanFlow typically requires samples from the target distribution to construct its target velocity field, which are unavailable in online RL. We propose Score-Based One-step MeanFlow Policy Optimization (SOM), an actor-critic algorithm that resolves this by constructing the target velocity field directly from the Q-function via score estimation and a probability flow ODE, thereby concentrating probability mass on high-value modes. In the fully online RL setting, SOM achieves state-of-the-art performance on locomotion tasks with a single generation step, while substantially reducing both training and inference time compared to prior diffusion- and flow-matching-based policies.