Pave-GRPO: Beyond Instantaneous Guidance through Principled Average Velocity Decomposition

Post-training via Group Relative Policy Optimization (GRPO) has emerged as a powerful paradigm for aligning flow-based generative models with human preferences. However, the iterative denoising nature of flow models incurs substantial costs when generating group rollouts for policy-gradient updates, compelling existing methods to train with extremely few denoising steps. This temporal sparsity severely restricts preference optimization: reward feedback can only reach a handful of stages per trajectory, leaving the vast majority of intermediate denoising steps without direct supervision and thus compromising alignment granularity. To address this, we propose Pave-GRPO, which reformulates the GRPO objective through Principled average velocity decomposition. Rather than generating expensive high-step rollouts, we maintain efficient few-step group sampling but decompose each coarse transition into an equivalent ensemble of finer sub-trajectories spanning multiple intermediate timesteps. This propagates reward feedback to a denser set of temporal stages for more comprehensive preference alignment without additional generation cost. This design offers two benefits: (i) zero-cost horizon expansion: through the direct reuse of piece-wise group samples and their associated rewards, Pave-GRPO significantly broadens the effective optimization scope under fixed sampling budgets; and (ii) comprehensive temporal supervision: by equivalently decomposing an instantaneous velocity target into a multi-timestep ensemble, it distributes reward signals across more intermediate stages of the denoising process, enabling finer-grained and more thorough preference optimization. Extensive experiments validate that Pave-GRPO effectively advances preference alignment across different reward settings, offering comprehensive performance enhancement.