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This arXiv preprint proposes a selection rule for the stochastic policy used when applying GRPO-style reinforcement learning to few-step flow generative models, choosing the policy that minimizes conditional KL for a given velocity update. It reports higher final reward than Flow-GRPO and Flow-CPS on 4-step image and video generation, but these are the authors' own benchmark results and have not been independently replicated. Readers working on RL fine-tuning of diffusion or flow models should check the derivation and the released code before relying on the gains.
Optimizing Stochastic Policy Geometry for Few-Step Flow Reinforcement Learning
arXiv:2610.41949v1 Announce Type: cross 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
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 this https URL
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2610.41949 [cs.AI]
(or arXiv:2610.41949v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2610.41949 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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