# DiffCPS: Diffusion Model based Constrained Policy Search for Offline Reinforcement Learning

arXiv: https://arxiv.org/abs/2310.05333 · HTML: https://mlsanity.com/paper/2310.05333/

## Key facts

- Cited by 28 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 51 of its 60 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Offline RL and imitation learning from data / [Diffusion and flow policies for offline RL](https://mlsanity.com/offlinerl/diffusion-and-flow-policies-for-offline-rl/)

## Builds on (most cited first, 30 of 51)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [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)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [AWAC: Accelerating Online Reinforcement Learning with Offline Datasets](https://mlsanity.com/paper/2006.09359/) (2020)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [MOReL : Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2005.05951/) (2020)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)

## Built on by (most cited first, 28 of 28)

- [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 Models for Reinforcement Learning: A Survey](https://mlsanity.com/paper/2311.01223/) (2023)
- [Energy-Weighted Flow Matching for Offline Reinforcement Learning](https://mlsanity.com/paper/2503.04975/) (2025)
- [Diffusion Guidance Is a Controllable Policy Improvement Operator](https://mlsanity.com/paper/2505.23458/) (2025)
- [DiffuserLite: Towards Real-time Diffusion Planning](https://mlsanity.com/paper/2401.15443/) (2024)
- [CleanDiffuser: An Easy-to-use Modularized Library for Diffusion Models in Decision Making](https://mlsanity.com/paper/2406.09509/) (2024)
- [Flow-Based Policy for Online Reinforcement Learning](https://mlsanity.com/paper/2506.12811/) (2025)
- [Q-learning with Adjoint Matching](https://mlsanity.com/paper/2601.14234/) (2026)
- [Scaling Offline RL via Efficient and Expressive Shortcut Models](https://mlsanity.com/paper/2505.22866/) (2025)
- [Deep Generative Models for Offline Policy Learning: Tutorial, Survey, and Perspectives on Future Directions](https://mlsanity.com/paper/2402.13777/) (2024)
- [AlignIQL: Policy Alignment in Implicit Q-Learning through Constrained Optimization](https://mlsanity.com/paper/2405.18187/) (2024)
- [Flow Policy Gradients for Robot Control](https://mlsanity.com/paper/2602.02481/) (2026)
- [Guided Flow Policy: Learning from High-Value Actions in Offline Reinforcement Learning](https://mlsanity.com/paper/2512.03973/) (2025)
- [Unleashing Flow Policies with Distributional Critics](https://mlsanity.com/paper/2509.23087/) (2025)
- [Flow Actor-Critic for Offline Reinforcement Learning](https://mlsanity.com/paper/2602.18015/) (2026)
- [Test-Time Gradient Guidance of Flow Policies in Reinforcement Learning](https://mlsanity.com/paper/2606.11087/) (2026)
- [Enhancing Exploration with Diffusion Policies in Hybrid Off-Policy RL: Application to Non-Prehensile Manipulation](https://mlsanity.com/paper/2411.14913/) (2024)
- [QPILOTS: Efficient Test-Time Q-Steering for Flow Policies](https://mlsanity.com/paper/2606.14801/) (2026)
- [Diffusion Models for Reinforcement Learning: Foundations, Taxonomy, and Development](https://mlsanity.com/paper/2510.12253/) (2025)
- [Entropy-Regularized Adjoint Matching for Offline Reinforcement Learning](https://mlsanity.com/paper/2605.06156/) (2026)
- [Dual-Flow Reinforcement Learning with State-Aware Exploration](https://mlsanity.com/paper/2606.29820/) (2026)
- [Noisy-Space Policy Gradient for Diffusion Policies in Offline Reinforcement Learning](https://mlsanity.com/paper/2609.06882/) (2026)
- [DiffPoGAN: Diffusion Policies with Generative Adversarial Networks for Offline Reinforcement Learning](https://mlsanity.com/paper/2406.09089/) (2024)
- [Forecasting in Offline Reinforcement Learning for Non-stationary Environments](https://mlsanity.com/paper/2512.01987/) (2025)
- [RoboTALES: Learning Reasoning-Guided Robot Policies via Task-Aligned Simulated Futures](https://mlsanity.com/paper/2607.06018/) (2026)
- [VINE: Taming Generative Control Policies for Reinforcement Learning](https://mlsanity.com/paper/2607.10369/) (2026)
- [Reinforcement Learning via Advantage Guidance](https://mlsanity.com/paper/2610.19783/) (2026)

## Abstract (arXiv)

Constrained policy search (CPS) is a fundamental problem in offline reinforcement learning, which is generally solved by advantage weighted regression (AWR). However, previous methods may still encounter out-of-distribution actions due to the limited expressivity of Gaussian-based policies. On the other hand, directly applying the state-of-the-art models with distribution expression capabilities (i.e., diffusion models) in the AWR framework is intractable since AWR requires exact policy probability densities, which is intractable in diffusion models. In this paper, we propose a novel approach, Diffusion-based Constrained Policy Search (dubbed DiffCPS), which tackles the diffusion-based constrained policy search with the primal-dual method. The theoretical analysis reveals that strong duality holds for diffusion-based CPS problems, and upon introducing parameter approximation, an approximated solution can be obtained after O(1/ε) number of dual iterations, where ε denotes the representation ability of the parametrized policy. Extensive experimental results based on the D4RL benchmark demonstrate the efficacy of our approach. We empirically show that DiffCPS achieves better or at least competitive performance compared to traditional AWR-based baselines as well as recent diffusion-based offline RL methods. The code is now available at https://github.com/felix-thu/DiffCPS.