On the Trajectory Regularity of ODE-based Diffusion Sampling

TL;DR

This paper investigates the trajectory properties of ODE-based diffusion sampling, revealing a shape-regular implicit denoising trajectory and proposing a dynamic time-scheduling method that improves image generation efficiency.

Contribution

It introduces a novel analysis of the sampling trajectories in diffusion models and proposes a simple, low-cost scheme to optimize the sampling schedule for better performance.

Findings

Trajectory regularity is observed in ODE-based diffusion sampling.

The proposed dynamic scheduling improves image quality with fewer function evaluations.

Minimal modifications to existing solvers are needed for implementation.

Abstract

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.