This paper explores the trajectory regularity in ODE-based diffusion sampling, a key component of generative models. The authors identify a strong shape regularity in the sampling trajectories, characterized by a linear-nonlinear-linear structure, regardless of the generated content. They explain this regularity through the analysis of an implicit denoising trajectory, which controls the rotation of the sampling trajectory. The denoising trajectory is shown to have a closed-form solution using kernel density estimation (KDE) with varying bandwidths. This insight leads to the development of a dynamic programming-based approach, called Geometry-Inspired Time Scheduling (GITS), to optimize the time schedule in sampling, improving image generation quality with minimal computational overhead. Experimental results demonstrate that GITS significantly enhances the performance of diffusion-based generative models, especially in a few function evaluations. The findings provide deeper understanding of the mechanisms behind diffusion models and open new avenues for more efficient sampling strategies.This paper explores the trajectory regularity in ODE-based diffusion sampling, a key component of generative models. The authors identify a strong shape regularity in the sampling trajectories, characterized by a linear-nonlinear-linear structure, regardless of the generated content. They explain this regularity through the analysis of an implicit denoising trajectory, which controls the rotation of the sampling trajectory. The denoising trajectory is shown to have a closed-form solution using kernel density estimation (KDE) with varying bandwidths. This insight leads to the development of a dynamic programming-based approach, called Geometry-Inspired Time Scheduling (GITS), to optimize the time schedule in sampling, improving image generation quality with minimal computational overhead. Experimental results demonstrate that GITS significantly enhances the performance of diffusion-based generative models, especially in a few function evaluations. The findings provide deeper understanding of the mechanisms behind diffusion models and open new avenues for more efficient sampling strategies.