Few‑step flow models generate samples with only a handful of large denoising transitions. Introducing GRPO to such models requires stochasticity in the denoising steps, and when a single step spans a wide noise range the resulting stochastic policy becomes a dominant factor in optimization. Existing constructions constrain the policy to preserve target flow coefficients, but this constraint admits a whole family of policies without a selection criterion. We propose Geo‑FSRL (Geometry‑Optimized Few‑Step Reinforcement Learning) built on a selection principle: for a fixed conditioning state‑timestep pair, choose the admissible policy that minimizes the conditional KL divergence induced by any non‑zero velocity‑output update. Within the coefficient‑preserving family of isotropic Gaussian transitions, this reduces to minimizing a single scalar geometry factor that determines the conditional KL for every velocity‑output update, the velocity‑space Fisher information, and the variance of the transition log‑likelihood‑ratio. We derive the unique closed‑form optimizer in this family, shared across all non‑zero update magnitudes and directions, with transition coefficients determined jointly by source and target noise levels. Because the minimized geometry factor still varies across timesteps, we further adopt gradient‑scale matching from prior work and obtain 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 while retaining a deterministic solver at inference. In the 4‑step setting, experiments on image and video generation models show higher final reward scores than Flow‑GRPO and Flow‑CPS. Code is released at https://github.com/ModelTC/LightX2V/tree/main/lightx2v_rl
Review: Geo‑FSRL eliminates policy ambiguity with a clear geometric criterion, achieving consistent optimization across tasks and delivering notable performance gains on few‑step flow models.