Flow-Map GRPO: Reinforcement Learning for Few-Step Flow-Map Generators via Anchored Stochastic Composition

Few-step flow-map generators, such as consistency models and MeanFlow, accelerate sampling by learning long-range transport maps between noise and data. However, their deterministic transitions do not directly provide the stochastic trajectories and tractable likelihood ratios required by reinforcement learning (RL) post-training. Existing SDE-based stochasticization techniques target velocity-based samplers and do not directly extend to long-range flow-map transitions. We propose Flow-Map GRPO, an online RL post-training framework for deterministic few-step flow-map generators. Its key component, Anchored Stochastic Flow Map Composition (ASFMC), combines deterministic transport with anchor-based conditional resampling. We establish the conditions under which this construction preserves the marginal probability path and develop tractable local- and endpoint-anchor policies for two-time and single-time flow maps. These policies enable a unified GRPO training procedure. Experiments on FLUX-based MeanFlow and sCM generators demonstrate substantial improvements in OCR, PickScore, and GenEval at different numbers of inference steps, including joint OCR--PickScore gains with mixed rewards. Controlled ablations show that the stochastic transition design is essential for translating training rewards into generation quality. Flow-Map GRPO enables effective RL alignment of pretrained deterministic flow-map generators while retaining their original parameterization, without retraining them as native stochastic models.