# Score Regularized Policy Optimization through Diffusion Behavior

arXiv: https://arxiv.org/abs/2310.07297 · HTML: https://mlsanity.com/paper/2310.07297/

## Key facts

- Cited by 71 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 30 of its 38 references that are in the map.
- First posted on arXiv 11 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 30)

- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [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)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [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)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [Imitating Human Behaviour with Diffusion Models](https://mlsanity.com/paper/2301.10677/) (2023)
- [Offline Reinforcement Learning with Fisher Divergence Critic Regularization](https://mlsanity.com/paper/2103.08050/) (2021)
- [Offline Reinforcement Learning via High-Fidelity Generative Behavior Modeling](https://mlsanity.com/paper/2209.14548/) (2022)
- [Efficient Diffusion Policies for Offline Reinforcement Learning](https://mlsanity.com/paper/2305.20081/) (2023)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference](https://mlsanity.com/paper/1703.09194/) (2017)
- [Supported Policy Optimization for Offline Reinforcement Learning](https://mlsanity.com/paper/2202.06239/) (2022)
- [Offline Reinforcement Learning with Soft Behavior Regularization](https://mlsanity.com/paper/2110.07395/) (2021)
- [Boosting Offline Reinforcement Learning via Data Rebalancing](https://mlsanity.com/paper/2210.09241/) (2022)
- [Know Your Boundaries: The Necessity of Explicit Behavioral Cloning in Offline RL](https://mlsanity.com/paper/2206.00695/) (2022)

## Built on by (most cited first, 30 of 71)

- [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)
- [One-Step Diffusion Policy: Fast Visuomotor Policies via Diffusion Distillation](https://mlsanity.com/paper/2410.21257/) (2024)
- [Energy-Weighted Flow Matching for Offline Reinforcement Learning](https://mlsanity.com/paper/2503.04975/) (2025)
- [RL-100: Performant Robotic Manipulation with Real-World Reinforcement Learning](https://mlsanity.com/paper/2510.14830/) (2025)
- [Diffusion Guidance Is a Controllable Policy Improvement Operator](https://mlsanity.com/paper/2505.23458/) (2025)
- [DiffuseLoco: Real-Time Legged Locomotion Control with Diffusion from Offline Datasets](https://mlsanity.com/paper/2404.19264/) (2024)
- [Diffusion Policies creating a Trust Region for Offline Reinforcement Learning](https://mlsanity.com/paper/2405.19690/) (2024)
- [Q-learning with Adjoint Matching](https://mlsanity.com/paper/2601.14234/) (2026)
- [Maximum Entropy Reinforcement Learning with Diffusion Policy](https://mlsanity.com/paper/2502.11612/) (2025)
- [RDT2: Exploring the Scaling Limit of UMI Data Towards Zero-Shot Cross-Embodiment Generalization](https://mlsanity.com/paper/2602.03310/) (2026)
- [Scaling Offline RL via Efficient and Expressive Shortcut Models](https://mlsanity.com/paper/2505.22866/) (2025)
- [Behavior-Regularized Diffusion Policy Optimization for Offline Reinforcement Learning](https://mlsanity.com/paper/2502.04778/) (2025)
- [AlignIQL: Policy Alignment in Implicit Q-Learning through Constrained Optimization](https://mlsanity.com/paper/2405.18187/) (2024)
- [One-Step Generative Policies with Q-Learning: A Reformulation of MeanFlow](https://mlsanity.com/paper/2511.13035/) (2025)
- [Langevin Soft Actor-Critic: Efficient Exploration through Uncertainty-Driven Critic Learning](https://mlsanity.com/paper/2501.17827/) (2025)
- [Variational Distillation of Diffusion Policies into Mixture of Experts](https://mlsanity.com/paper/2406.12538/) (2024)
- [Diffusion Spectral Representation for Reinforcement Learning](https://mlsanity.com/paper/2406.16121/) (2024)
- [Falcon: Fast Visuomotor Policies via Partial Denoising](https://mlsanity.com/paper/2503.00339/) (2025)
- [Prior-Guided Diffusion Planning for Offline Reinforcement Learning](https://mlsanity.com/paper/2505.10881/) (2025)
- [ReAlign: Text-to-Motion Generation via Step-Aware Reward-Guided Alignment](https://mlsanity.com/paper/2511.19217/) (2025)
- [Aligning Diffusion Behaviors with Q-functions for Efficient Continuous Control](https://mlsanity.com/paper/2407.09024/) (2024)
- [One-Step Flow Q-Learning: Addressing the Diffusion Policy Bottleneck in Offline Reinforcement Learning](https://mlsanity.com/paper/2508.13904/) (2025)
- [Multi-agent Coordination via Flow Matching](https://mlsanity.com/paper/2511.05005/) (2025)
- [From Prior to Pro: Efficient Skill Mastery via Distribution Contractive RL Finetuning](https://mlsanity.com/paper/2603.10263/) (2026)
- [Composite Flow Matching for Reinforcement Learning with Shifted-Dynamics Data](https://mlsanity.com/paper/2505.23062/) (2025)
- [Motus2: A Self-Evolving General World Model for Dexterous Manipulation](https://mlsanity.com/paper/2608.30237/) (2026)
- [Unleashing Flow Policies with Distributional Critics](https://mlsanity.com/paper/2509.23087/) (2025)
- [Habitizing Diffusion Planning for Efficient and Effective Decision Making](https://mlsanity.com/paper/2502.06401/) (2025)
- [The Duality of Generative AI and Reinforcement Learning in Robotics: A Review](https://mlsanity.com/paper/2410.16411/) (2024)

## Abstract (arXiv)

Recent developments in offline reinforcement learning have uncovered the immense potential of diffusion modeling, which excels at representing heterogeneous behavior policies. However, sampling from diffusion policies is considerably slow because it necessitates tens to hundreds of iterative inference steps for one action. To address this issue, we propose to extract an efficient deterministic inference policy from critic models and pretrained diffusion behavior models, leveraging the latter to directly regularize the policy gradient with the behavior distribution's score function during optimization. Our method enjoys powerful generative capabilities of diffusion modeling while completely circumventing the computationally intensive and time-consuming diffusion sampling scheme, both during training and evaluation. Extensive results on D4RL tasks show that our method boosts action sampling speed by more than 25 times compared with various leading diffusion-based methods in locomotion tasks, while still maintaining state-of-the-art performance.