Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policies

• URL: http://arxiv.org/abs/2601.08136v1
• Date: Tue, 13 Jan 2026 01:58:24 GMT
• Title: Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policies
• Authors: Zeyang Li, Sunbochen Tang, Navid Azizan,
• Abstract summary: We propose a unified framework, reverse flow matching (RFM), which rigorously addresses the problem of training diffusion and flow models without direct target samples.<n>By adopting a reverse inferential perspective, we formulate the training target as a posterior mean estimation problem given an intermediate noisy sample.<n>We show that existing noise-expectation and gradient-expectation methods are two specific instances within this broader class.
• Score: 4.249024052507976
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Diffusion and flow policies are gaining prominence in online reinforcement learning (RL) due to their expressive power, yet training them efficiently remains a critical challenge. A fundamental difficulty in online RL is the lack of direct samples from the target distribution; instead, the target is an unnormalized Boltzmann distribution defined by the Q-function. To address this, two seemingly distinct families of methods have been proposed for diffusion policies: a noise-expectation family, which utilizes a weighted average of noise as the training target, and a gradient-expectation family, which employs a weighted average of Q-function gradients. Yet, it remains unclear how these objectives relate formally or if they can be synthesized into a more general formulation. In this paper, we propose a unified framework, reverse flow matching (RFM), which rigorously addresses the problem of training diffusion and flow models without direct target samples. By adopting a reverse inferential perspective, we formulate the training target as a posterior mean estimation problem given an intermediate noisy sample. Crucially, we introduce Langevin Stein operators to construct zero-mean control variates, deriving a general class of estimators that effectively reduce importance sampling variance. We show that existing noise-expectation and gradient-expectation methods are two specific instances within this broader class. This unified view yields two key advancements: it extends the capability of targeting Boltzmann distributions from diffusion to flow policies, and enables the principled combination of Q-value and Q-gradient information to derive an optimal, minimum-variance estimator, thereby improving training efficiency and stability. We instantiate RFM to train a flow policy in online RL, and demonstrate improved performance on continuous-control benchmarks compared to diffusion policy baselines.

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