# Policy Representation via Diffusion Probability Model for Reinforcement Learning

arXiv: https://arxiv.org/abs/2305.13122 · HTML: https://mlsanity.com/paper/2305.13122/

## Key facts

- Cited by 112 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 60 of its 98 references that are in the map.
- First posted on arXiv 22 May 2023.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 60)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [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)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [A Generalist Agent](https://mlsanity.com/paper/2205.06175/) (2022)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Learning Robust Rewards with Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1710.11248/) (2017)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [Imitating Human Behaviour with Diffusion Models](https://mlsanity.com/paper/2301.10677/) (2023)

## Built on by (most cited first, 30 of 112)

- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [Steering Your Diffusion Policy with Latent Space Reinforcement Learning](https://mlsanity.com/paper/2506.15799/) (2025)
- [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)
- [Diffusion Models for Reinforcement Learning: A Survey](https://mlsanity.com/paper/2311.01223/) (2023)
- [From Imitation to Refinement -- Residual RL for Precise Assembly](https://mlsanity.com/paper/2407.16677/) (2024)
- [Policy Agnostic RL: Offline RL and Online RL Fine-Tuning of Any Class and Backbone](https://mlsanity.com/paper/2412.06685/) (2024)
- [Efficient Online Reinforcement Learning for Diffusion Policy](https://mlsanity.com/paper/2502.00361/) (2025)
- [SkillDiffuser: Interpretable Hierarchical Planning via Skill Abstractions in Diffusion-Based Task Execution](https://mlsanity.com/paper/2312.11598/) (2023)
- [Policy Decorator: Model-Agnostic Online Refinement for Large Policy Model](https://mlsanity.com/paper/2412.13630/) (2024)
- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [DIME:Diffusion-Based Maximum Entropy Reinforcement Learning](https://mlsanity.com/paper/2502.02316/) (2025)
- [Diffusion Guidance Is a Controllable Policy Improvement Operator](https://mlsanity.com/paper/2505.23458/) (2025)
- [Learning Multimodal Behaviors from Scratch with Diffusion Policy Gradient](https://mlsanity.com/paper/2406.00681/) (2024)
- [DiffuseLoco: Real-Time Legged Locomotion Control with Diffusion from Offline Datasets](https://mlsanity.com/paper/2404.19264/) (2024)
- [Boosting Continuous Control with Consistency Policy](https://mlsanity.com/paper/2310.06343/) (2023)
- [Scaling Diffusion Policy in Transformer to 1 Billion Parameters for Robotic Manipulation](https://mlsanity.com/paper/2409.14411/) (2024)
- [Flow-Based Policy for Online Reinforcement Learning](https://mlsanity.com/paper/2506.12811/) (2025)
- [Maximum Entropy Reinforcement Learning with Diffusion Policy](https://mlsanity.com/paper/2502.11612/) (2025)
- [Diffusion Tree Sampling: Scalable inference-time alignment of diffusion models](https://mlsanity.com/paper/2506.20701/) (2025)
- [EXPO: Stable Reinforcement Learning with Expressive Policies](https://mlsanity.com/paper/2507.07986/) (2025)
- [Diffusion Actor-Critic: Formulating Constrained Policy Iteration as Diffusion Noise Regression for Offline Reinforcement Learning](https://mlsanity.com/paper/2405.20555/) (2024)
- [DiWA: Diffusion Policy Adaptation with World Models](https://mlsanity.com/paper/2508.03645/) (2025)
- [M2Diffuser: Diffusion-based Trajectory Optimization for Mobile Manipulation in 3D Scenes](https://mlsanity.com/paper/2410.11402/) (2024)
- [floq: Training Critics via Flow-Matching for Scaling Compute in Value-Based RL](https://mlsanity.com/paper/2509.06863/) (2025)
- [One-Step Flow Policy Mirror Descent](https://mlsanity.com/paper/2507.23675/) (2025)
- [UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Control](https://mlsanity.com/paper/2502.05749/) (2025)
- [GenPO: Generative Diffusion Models Meet On-Policy Reinforcement Learning](https://mlsanity.com/paper/2505.18763/) (2025)
- [Discrete Policy: Learning Disentangled Action Space for Multi-Task Robotic Manipulation](https://mlsanity.com/paper/2409.18707/) (2024)

## Abstract (arXiv)

Popular reinforcement learning (RL) algorithms tend to produce a unimodal policy distribution, which weakens the expressiveness of complicated policy and decays the ability of exploration. The diffusion probability model is powerful to learn complicated multimodal distributions, which has shown promising and potential applications to RL. In this paper, we formally build a theoretical foundation of policy representation via the diffusion probability model and provide practical implementations of diffusion policy for online model-free RL. Concretely, we character diffusion policy as a stochastic process, which is a new approach to representing a policy. Then we present a convergence guarantee for diffusion policy, which provides a theory to understand the multimodality of diffusion policy. Furthermore, we propose the DIPO which is an implementation for model-free online RL with DIffusion POlicy. To the best of our knowledge, DIPO is the first algorithm to solve model-free online RL problems with the diffusion model. Finally, extensive empirical results show the effectiveness and superiority of DIPO on the standard continuous control Mujoco benchmark.