# Distributional Reinforcement Learning with Diffusion Bridge Critics

arXiv: https://arxiv.org/abs/2602.05783 · HTML: https://mlsanity.com/paper/2602.05783/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL with diffusion and flow models, one of 15 directions in Deep reinforcement learning methods.
- Builds on 36 of its 42 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

- 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 36)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [BBDM: Image-to-image Translation with Brownian Bridge Diffusion Models](https://mlsanity.com/paper/2205.07680/) (2022)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Controlling Overestimation Bias with Truncated Mixture of Continuous Distributional Quantile Critics](https://mlsanity.com/paper/2005.04269/) (2020)
- [Learning a Diffusion Model Policy from Rewards via Q-Score Matching](https://mlsanity.com/paper/2312.11752/) (2023)
- [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)
- [Flow Matching Policy Gradients](https://mlsanity.com/paper/2507.21053/) (2025)
- [Diffusion Actor-Critic with Entropy Regulator](https://mlsanity.com/paper/2405.15177/) (2024)
- [Distributional Soft Actor-Critic: Off-Policy Reinforcement Learning for Addressing Value Estimation Errors](https://mlsanity.com/paper/2001.02811/) (2020)
- [Efficient Online Reinforcement Learning for Diffusion Policy](https://mlsanity.com/paper/2502.00361/) (2025)
- [DIME:Diffusion-Based Maximum Entropy Reinforcement Learning](https://mlsanity.com/paper/2502.02316/) (2025)
- [Image Restoration Through Generalized Ornstein-Uhlenbeck Bridge](https://mlsanity.com/paper/2312.10299/) (2023)
- [Distributional Soft Actor-Critic with Three Refinements](https://mlsanity.com/paper/2310.05858/) (2023)
- [Generative Modeling with Phase Stochastic Bridges](https://mlsanity.com/paper/2310.07805/) (2023)
- [floq: Training Critics via Flow-Matching for Scaling Compute in Value-Based RL](https://mlsanity.com/paper/2509.06863/) (2025)
- [UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Control](https://mlsanity.com/paper/2502.05749/) (2025)

## Abstract (arXiv)

Recent advances in diffusion-based reinforcement learning (RL) methods have demonstrated promising results in a wide range of continuous control tasks. However, existing works in this field focus on the application of diffusion policies while leaving the diffusion critics unexplored. In fact, since policy optimization fundamentally relies on the critic, accurate value estimation is far more important than policy expressiveness. Furthermore, given the stochasticity of most reinforcement learning tasks, it has been confirmed that the critic is more appropriately depicted with a distributional model. Motivated by these points, we propose a novel distributional RL method with Diffusion Bridge Critics (DBC). DBC directly models the inverse cumulative distribution function (CDF) of the Q value. This allows us to accurately capture the value distribution and prevents it from collapsing into a trivial Gaussian distribution owing to the strong distribution-matching capability of the diffusion bridge. Moreover, we further derive an analytic integral formula to address discretization errors in DBC, which is essential in value estimation. To our knowledge, DBC is the first work to employ the diffusion bridge model as the critic. Notably, DBC is also a plug-and-play component and can be integrated into most existing RL frameworks. Experimental results on MuJoCo robot control benchmarks demonstrate the superiority of DBC compared with previous distributional critic models.