TamedFlow: Trajectory-Aware Distillation\\for Teacher-Assisted Diffusion Sampling

Diffusion Transformers (DiTs) deliver high-fidelity image and video generation, but inference requires many sequential model evaluations. Two acceleration strategies are increasingly important: model compression makes each evaluation cheaper, while adaptive inference avoids selected teacher computation through reuse, forecasting, or speculative execution. Their combination, however, is brittle: directly applying the evaluated adaptive methods to a compressed student can degrade quality, an observed failure mode we call the \textbf{Combination Gap}. We link this gap to a mismatch between pointwise distillation and short-horizon execution: a student trained at teacher states need not remain reliable when its own predictions are chained. We propose \textbf{TamedFlow}, which trains a compressed DiT for this deployed role through cross-architecture feature alignment, a near-identity Velocity Alignment Head, and randomized rollout supervision. At inference, a lightweight Learnable Trajectory Estimator routes completed drafts: accepted drafts bypass the teacher, while rejected drafts roll back and receive one teacher rescue step. Distilling DiT-XL/2 into DiT-B/2, TamedFlow reaches FID $2.58$ at $2.25\times$ measured speedup over DDIM-50 on ImageNet $256\times256$. Ablations support trajectory supervision, and routing controls favor LTE over random decisions at nearly matched latency. Evaluations on ImageNet $512\times512$, MS-COCO, and Latte/FaceForensics extend the empirical scope.