Residual-Guided Sampling: Structured Acceleration and Timestep Scheduling

Efficient sampling from diffusion and flow models depends jointly on numerical updates and timestep schedules, yet these components are often designed separately. We introduce residual-guided sampling to unify them through a structural residual. For smooth linear data-noise interpolants, pathwise forward acceleration lies in the state-velocity span under a nondegeneracy condition. For the variance-preserving cosine interpolant, augmenting Euler with a second-order acceleration term whose state and velocity coefficients are derived from the forward interpolant recovers deterministic DDIM through second order. However, reverse-trajectory acceleration need not lie in this span, so we approximate it as a weighted sum of state and velocity. With the pretrained velocity field fixed, a lightweight head predicts the two coefficients from time, conditioning, and guidance scale. The resulting acceleration mismatch defines a computable residual. Our analysis shows that it characterizes the leading discretization defect and enters a global error bound; it also guides coefficient fitting and a propagation-aware timestep schedule. The sampler uses the predicted acceleration without extra velocity-field evaluations, while the schedule transfers to other integrators. A single head supports unconditional and conditional sampling with or without classifier-free guidance. Across tested settings, our method improves upon matched Euler, Heun, AB2, and RF-Solver baselines, with the largest gains at low-to-intermediate evaluation budgets.