  The diffusion model has shown remarkable success in computer vision, but it
remains unclear whether the ODE-based probability flow or the SDE-based
diffusion model is more superior and under what circumstances. Comparing the
two is challenging due to dependencies on data distributions, score training,
and other numerical issues. In this paper, we study the problem mathematically
for two limiting scenarios: the zero diffusion (ODE) case and the large
diffusion case. We first introduce a pulse-shape error to perturb the score
function and analyze error accumulation of sampling quality, followed by a
thorough analysis for generalization to arbitrary error. Our findings indicate
that when the perturbation occurs at the end of the generative process, the ODE
model 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 a
pulse-shape perturbation is exponentially suppressed as the diffusion term's
magnitude increases to infinity. Numerical validation of this phenomenon is
provided using Gaussian, Gaussian mixture, and Swiss roll distribution, as well
as realistic datasets like MNIST and CIFAR-10.
