Geometry-Aware Time Reparameterization for Flow-Map Distillation

Few-step flow-map generators, including MeanFlow and consistency models, enable efficient sampling through long-range transport, yet their on-policy distillation remains underexplored. We introduce FlowMap-OPD, an on-policy distillation framework that separates student-state acquisition from teacher--student distribution comparison. A formulation based on state marginals establishes this separation, while flow--velocity consistency connects local supervision to the deployed long-range map. Within this framework, we develop flow-map, induced-velocity, and instantaneous-velocity distribution supervision, each paired with a separately specified native flow-map rollout. Cross-capacity ImageNet experiments across three teacher rewards identify instantaneous-velocity distribution supervision with independently tunable student consistency as the most effective choice. In text-to-image experiments, FlowMap-OPD demonstrates strong multi-specialist consolidation capabilities and surpasses multi-reward Flow-Map GRPO in task performance and convergence speed.

Flow and diffusion models suffer from slow inference due to computationally expensive numerical integration. Distillation provides a promising way for a student model to learn from a teacher's dynamics, enabling one-step or few-step generation. However, existing methods often depend on curated distillation datasets, costly teacher rollouts, or auxiliary proxy networks, which complicate model training and scaling. In this work, we propose Consistent Distribution Matching, a simulation-free and data-free distillation method for accelerating diffusion and flow models while preserving strong generative capacity. Our key insight is to unify sample generation and score estimation with one student network. Thus, our framework uses only two models, a frozen teacher and a trainable student, and optimizes one objective. We prove that minimizing our objective indicates Wasserstein convergence of the student flow-map pushforwards to the teacher marginals. On ImageNet 256$\times$256, our method attains an FID of 2.04 with a single function evaluation (1-NFE) and a 4-NFE FID of 1.37 within 40 epochs of training, surpassing the state-of-the-art distillation baselines without data. Our code code and model are available at https://consistentdmd.github.io/.

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 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 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.