BoundaryDelta: Spline-Integrated Average-Velocity Prediction for Efficient Diffusion Sampling

Cache-based acceleration for diffusion and flow-matching models typically reuses or extrapolates an instantaneous prediction, even though each solver step depends on velocity accumulated over an interval. We introduce BoundaryDelta, a training-free framework that instead estimates the interval-average velocity. At each cached step, BoundaryDelta constructs a causal, boundary-constrained cubic Hermite velocity surrogate from completed model evaluations, then integrates it analytically to advance without an additional transformer call. Because approximation quality depends on where genuine evaluations occur, we couple this controller with budget-specific anchor schedules found offline. Across Qwen-Image and Stable Diffusion 3.5 Medium, BoundaryDelta delivers the strongest overall FULL-reference fidelity among equal-NFE baselines across aggressive and moderate call budgets. In a separate image-conditioned 3D study, BoundaryDelta retains FULL-50-level held-out ground-truth geometry for Hunyuan3D-Shape-v2.1 Small using 17 of 50 transformer evaluations. On Qwen-Image, BoundaryDelta reduces transformer evaluations by 50–80% at the primary 10-, 17-, and 25-call settings and achieves up to $4.72\times$ paired steady-state speedup.