Accelerating Diffusion Sampling with Optimized Time Steps

Diffusion probabilistic models (DPMs) have shown remarkable performance in high-resolution image synthesis, but their sampling efficiency is still to be desired due to the typically large number of sampling steps. Recent advancements in high-order numerical ODE solvers for DPMs have enabled the generation of high-quality images with much fewer sampling steps. While this is a significant development, most sampling methods still employ uniform time steps, which is not optimal when using a small number of steps. To address this issue, we propose a general framework for designing an optimization problem that seeks more appropriate time steps for a specific numerical ODE solver for DPMs. This optimization problem aims to minimize the distance between the ground-truth solution to the ODE and an approximate solution corresponding to the numerical solver. It can be efficiently solved using the constrained trust region method, taking less than $15$ seconds. Our extensive experiments on both unconditional and conditional sampling using pixel- and latent-space DPMs demonstrate that, when combined with the state-of-the-art sampling method UniPC, our optimized time steps significantly improve image generation performance in terms of FID scores for datasets such as CIFAR-10 and ImageNet, compared to using uniform time steps.