Reverse Flow Matching: A Unified Framework for Training Diffusion and Flow Policies in Online Reinforcement Learning
Researchers propose Reverse Flow Matching (RFM), a unified mathematical framework that addresses the challenge of training diffusion and flow models in online reinforcement learning without direct samples from the target distribution. The framework reconciles two previously distinct training approaches—noise-expectation and gradient-expectation methods—by formulating training as a posterior mean estimation problem using Langevin Stein operators. This theoretical unification enables more efficient and stable training of flow policies and demonstrates improved performance on continuous-control benchmarks.
The paper addresses a fundamental challenge in online reinforcement learning: training diffusion and flow policies efficiently when direct samples from the target Boltzmann distribution (defined by the Q-function) are unavailable. Previous work developed two seemingly separate families of methods—noise-expectation approaches using weighted averages of noise, and gradient-expectation approaches using weighted averages of Q-function gradients—but their formal relationship remained unclear. The authors propose Reverse Flow Matching, which adopts a reverse inferential perspective to formulate the problem as posterior mean estimation given an intermediate noisy sample. Using Langevin Stein operators, they construct zero-mean control variates that generate a general class of estimators sharing the same expectation, revealing that existing methods are specific instances of this broader framework. The unified view extends Boltzmann distribution targeting from diffusion to flow policies and enables principled combination of Q-value and Q-gradient information, improving training efficiency and stability. Empirical results on continuous-control benchmarks show improved performance compared to diffusion policy baselines.
What's missing
The paper does not discuss computational complexity or scalability implications of the Langevin Stein operator construction compared to existing methods. Additionally, while continuous-control benchmarks are mentioned, specific benchmark names, numerical comparisons, and statistical significance testing details are not provided in the abstract.
What different sources said
- arXiv cs.LGCenter
Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policies
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