  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.
