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The diffusion model has shown remarkable success in computer vision, but itremains unclear whether the ODE-based probability flow or the SDE-baseddiffusion model is more superior and under what circumstances. Comparing thetwo is challenging due to dependencies on data distributions, score training,and other numerical issues. In this paper, we study the problem mathematicallyfor two limiting scenarios: the zero diffusion (ODE) case and the largediffusion case. We first introduce a pulse-shape error to perturb the scorefunction and analyze error accumulation of sampling quality, followed by athorough analysis for generalization to arbitrary error. Our findings indicatethat when the perturbation occurs at the end of the generative process, the ODEmodel outperforms the SDE model with a large diffusion coefficient. However,when the perturbation occurs earlier, the SDE model outperforms the ODE model,and we demonstrate that the error of sample generation due to such apulse-shape perturbation is exponentially suppressed as the diffusion term'smagnitude increases to infinity. Numerical validation of this phenomenon isprovided using Gaussian, Gaussian mixture, and Swiss roll distribution, as wellas realistic datasets like MNIST and CIFAR-10.

Exploring the Optimal Choice for Generative Processes in Diffusion Models: Ordinary vs Stochastic Differential Equations