Expressiveness Remarks for Denoising Diffusion Models and Samplers
Francisco Vargas Teodora Reu Anna Kerekes
Denoising diffusion models are a class of generative models which have
recently achieved state-of-the-art results across many domains. Gradual noise
is added to the data using a diffusion process, which transforms the data
distribution into a Gaussian. Samples from the generative model are then
obtained by simulating an approximation of the time reversal of this diffusion
initialized by Gaussian samples. Recent research has explored adapting
diffusion models for sampling and inference tasks. In this paper, we leverage
known connections to stochastic control akin to the F\"ollmer drift to extend
established neural network approximation results for the F\"ollmer drift to
denoising diffusion models and samplers.