Flow Matching Reinforcement Learning via SDE Inference

We develop a unified framework for flow-based reinforcement learning (RL) grounded in diffusion–flow duality and establish its theoretical foundations. The frameworks enables RL for deterministic flow matching inference by introducing diffusion stochastic inference dynamics that supports exploration while admitting deterministic deployment. We show that our frameworks subsumes several existing flow-based RL methods as special cases and inspire effective now methods. Then we provide theoretical foundations for the frameworks by establishing the correctness and performance transfer guarantee. Specifically, we prove that the policies optimized under stochastic dynamics close to deterministic dynamics at deployment when the pretrained model is well-trained. Moreover, we show that the policy improvement achieved under training-time SDE inference transfers to deployment-time ODE inference. Finally, we conduct experiments to validate our theoretical results.