Geo-FSRL: Geometry-Optimized Few-Step Flow Reinforcement Learning

arXiv:2610.41949v1 Announce Type: new Abstract: Few-step flow models generate samples through a handful of large denoising transitions. Applying GRPO to such models requires introducing stochasticity into the denoising transitions, and when a single transition spans a wide range of noise levels, the choice of the resulting stochastic policy becomes a major factor in optimization. Recent constructions constrain the policy to preserve the target flow coefficients, but this constraint admits a family of policies and offers no criterion for choosing among them. We introduce Geo-FSRL (Geometry-Optimized Few-Step Reinforcement Learning), built on a selection principle: at a fixed conditioning state and timestep pair, choose the admissible policy that minimizes the conditional KL divergence induced by any given nonzero velocity-output update. Within a coefficient-preserving family of isotropic Gaussian transitions, this criterion reduces to minimizing a single scalar geometry factor that determines the conditional KL for every velocity-output update. The same factor governs velocity-space Fisher information and conditional transition log-likelihood-ratio variance. We derive the unique closed-form optimizer within this family, shared across all nonzero update magnitudes and directions, with transition coefficients determined by both the source and target noise levels. Because the minimized geometry factor still varies across timesteps, we further adopt gradient-scale matching from prior work and derive closed-form policy-gradient and KL weights that normalize explicit score scales and reference-KL curvature. Geo-FSRL trains on the original few-step schedule and retains the deterministic solver at inference. Our method achieves higher final reward scores than Flow-GRPO and Flow-CPS on both image generation and video generation models under the 4-step setting. Code is available at https://github.com/ModelTC/LightX2V/tree/main/lightx2v_rl