Accelerating Diffusion Models with Physical Velocity Evolution

Diffusion and flow-based generative models deliver strong visual synthesis quality but incur substantial inference cost during iterative sampling. Existing caching methods typically rely on high-dimensional feature differences that can entangle content and noise, overlooking the physical-time velocity dynamics underlying the generative ODE. These representation-level differences do not directly characterize the physical evolution of the latent state, which is governed by a velocity field over continuous sampling time. Instead, grounding cache reuse in physical-time velocity dynamics connects approximation errors to the latent updates they perturb, with the actual physical time intervals determining how velocity errors translate into trajectory deviations. Based on this observation, we introduce Trajectory-Aligned Flow Caching (TAFC), a training-free framework that operationalizes physical-time velocity dynamics through three complementary components. Physical-Time velocity Extrapolation predicts upcoming latent updates by extrapolating velocity dynamics over physical sampling intervals. Curvature-Aware Reuse Gating uses velocity curvature to assess whether the observed dynamics support continued local extrapolation. Self-Calibrating Error Feedback measures a posteriori approximation errors at refresh steps and adapts reuse tolerances, calibrating physical trajectory predictions against model-evaluated updates. Together, these components connect physical-time velocity dynamics, prediction reliability, and online error correction in a closed-loop caching framework. Extensive experiments on large-scale image and video generative models demonstrate that TAFC achieves favorable efficiency–fidelity trade-offs over existing training-free caching methods.