Nearly $d$-Linear Convergence Bounds for Diffusion Models via Stochastic Localization

arXiv:2308.03686v3 Announce Type: replace-cross
Abstract: Denoising diffusions are a powerful method to generate approximate samples from high-dimensional data distributions. Recent results provide polynomial bounds on their convergence rate, assuming $L^2$-accurate scores. Until now, the tightest bounds were either superlinear in the data dimension or required strong smoothness assumptions. We provide the first convergence bounds which are linear in the data dimension (up to logarithmic factors) assuming only finite second moments of the data distribution. We show that diffusion models require …

abstract arxiv assumptions convergence cs.lg data denoising diffusion diffusion models generate linear localization polynomial rate results samples stat.ml stochastic type via