  Diffusion-based generative models use stochastic differential equations
(SDEs) and their equivalent ordinary differential equations (ODEs) to establish
a smooth connection between a complex data distribution and a tractable prior
distribution. In this paper, we identify several intriguing trajectory
properties in the ODE-based sampling process of diffusion models. We
characterize an implicit denoising trajectory and discuss its vital role in
forming the coupled sampling trajectory with a strong shape regularity,
regardless of the generated content. We also describe a dynamic
programming-based scheme to make the time schedule in sampling better fit the
underlying trajectory structure. This simple strategy requires minimal
modification to any given ODE-based numerical solvers and incurs negligible
computational cost, while delivering superior performance in image generation,
especially in $5\sim 10$ function evaluations.
