JAGG: Jacobian-Aggregated Group Gradient for Efficient GRPO Training of Diffusion Models

Group Relative Policy Optimization (GRPO) is a powerful reinforcement learning algorithm for aligning generative models with human preferences. While successful in large language models~\cite{shao2024deepseekmathpushinglimitsmathematical}, its extension to diffusion and flow matching models introduces a severe computational bottleneck: gradients must be back-propagated through the high-capacity DiT backbone at \emph{every} timestep of the sampling trajectory, making high-resolution text-to-image (T2I) training prohibitively expensive. Training-free DiT inference acceleration methods (e.g., $\mathrm{\Delta }$-DiT, ScalingCache) exploit the fact that DiT hidden states and velocity predictions vary \emph{smoothly and nearly linearly} along the trajectory. We ask whether the same linearity can reduce the backward-pass cost of DiT RL training, and answer affirmatively with $\mathbf{\text{JAGG}}$ ($\mathbf{\text{J}}$acobian-$\mathbf{\text{A}}$ggregated $\mathbf{\text{G}}$roup $\mathbf{\text{G}}$radient), which reduces full transformer backward passes from $W$ to $2$ per group of $W$ consecutive steps. JAGG approximates intermediate-step Jacobians via $t$-weighted interpolation of the endpoint Jacobians, then aggregates per-step upstream signals into two composite gradients applied through a single joint backward pass. We prove this interpolation is \emph{exact} when the velocity is linear in $(z,t)$, and a cosine-similarity routing rule ($\mathtt{\text{jagg\_frac}}$) deploys JAGG only where the assumption holds. Experiments on T2I benchmarks show JAGG delivers $\sim$2$\times$ backward speedup with negligible quality degradation.