Explicit Error Propagation for Improving Timestep Scheduling of Generative Models

Discrete timestep schedules are among the last heuristic components of diffusion and flow-based samplers. Common choices, such as time-uniform and logSNR-uniform, rely on unrealistic simplifying assumptions: locally stationary score errors, slowly varying noise levels, and uniform error propagation along the sampling trajectory. We introduce EP-Flow, a principled framework for timestep scheduling based on explicit error propagation. By modeling the sampler as a discrete-time dynamical system, we derive a tractable surrogate functional decomposing total generation error into three components: (i) a persistent directional bias arising from score approximation error, (ii) a residual variance from step-local stochastic error, and (iii) a local truncation error. Each component is weighted by trajectory-dependent propagators quantifying how errors at each step accumulate at the final sample. This objective applies to any initial schedule: EP-Flow both improves heuristic spacings and provides a complementary signal for refining already-learned ones. Across four standard datasets—CIFAR-10, FFHQ, AFHQv2, and ImageNet-64—EP-Flow consistently improves few-step generation over the widely used Karras schedule. It generalizes across training recipes (EDM2), refines learned schedules in Stable Diffusion v1.5, and extends to large-scale text-to-image generation with FLUX.1-dev.