Defect-Guided Time-Warp Flow Distillation for Semigroup-Robust Fast Diffusion Generation

Fast diffusion generation has been improved through few-step distillation, and trajectory rectification. However, a central difficulty remains: a student model only trained on single-step transitions is deployed via repeated composition across different step counts. This resulting discrepancy between a direct transition and its multi-step composition is defined as the semigroup defect. We therefore recast fast diffusion distillation as a time-geometry adaptation problem, where temporal allocation along the trajectory is optimized instead of explicitly modifying the state-space path. Specifically, we propose Defect-Guided Time-Warp Flow Distillation (DG-TWFD), which jointly learns a continuous-time student flow map and a monotone time warp that reallocates temporal resolution toward teacher regions with high compositional difficulty. Training integrates teacher flow matching with defect-aware optimization and a time-warped curriculum. We evaluate our method on unconditional CIFAR-10 and ImageNet-64, achieving competitive Fréchet Inception Distance (FID) and Inception Score (IS) on CIFAR-10, and FID and recall on ImageNet-64 across different inference step settings. Our best results are 1.81 FID / 9.87 IS on CIFAR-10 and 2.49 FID / 0.67 recall on ImageNet-64. All code and data used in this work are available at https://anonymous.4open.science/r/DGTW-code-base-95F0/Anonymous Github link.