# Scalable Maximum Entropy Reinforcement Learning for Diffusion Policies via Adjoint Matching

arXiv: https://arxiv.org/abs/2606.22630 · HTML: https://mlsanity.com/paper/2606.22630/

## Key facts

- Cited by 5 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 96 of its 116 references that are in the map.
- First posted on arXiv 21 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 96)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [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)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [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)
- [dm_control: Software and Tasks for Continuous Control](https://mlsanity.com/paper/2006.12983/) (2020)
- [ManiSkill2: A Unified Benchmark for Generalizable Manipulation Skills](https://mlsanity.com/paper/2302.04659/) (2023)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [ManiSkill3: GPU Parallelized Robotics Simulation and Rendering for Generalizable Embodied AI](https://mlsanity.com/paper/2410.00425/) (2024)

## Built on by (most cited first, 5 of 5)

- [Expressivity and Statistical Trade-offs in Diffusion Policy Learning](https://mlsanity.com/paper/2607.07967/) (2026)
- [Uncertainty-Gated Exploration Noise Suppresses Task Collapse in Online RL Fine-Tuning of a Flow-Matching Vision-Language-Action Policy](https://mlsanity.com/paper/2609.28838/) (2026)
- [Constrained Flow Policy Updates: A Generalized Schr"odinger Bridge View](https://mlsanity.com/paper/2609.32952/) (2026)
- [Diffusion Policy Improvement with Proposal-Conditioned Refinement Flows](https://mlsanity.com/paper/2609.36812/) (2026)
- [Reinforcement Learning via Fixed-point Flow Matching](https://mlsanity.com/paper/2610.12848/) (2026)

## Abstract (arXiv)

Diffusion policies have recently emerged as a powerful paradigm for representing complex action distributions in reinforcement learning (RL). However, their application to online RL remains limited by the challenge of scalable training in the absence of ground-truth data, where standard optimization techniques such as score matching are not directly applicable. In this work, we introduce a highly efficient algorithm for optimizing diffusion policies by leveraging recent advances in stochastic optimal control. Our approach is based on adjoint matching, which enables simulation-free training and circumvents the need for explicit likelihood estimation or costly backpropagation through the diffusion process. Furthermore, we propose several extensions that improve the robustness and stability of the method in practical settings. Empirical results demonstrate that our approach achieves competitive performance while significantly reducing computational overhead, making diffusion policies more viable for online RL scenarios.