To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models

TL;DR

This paper explores the theoretical guarantees and insights of score matching in denoising diffusion models, connecting them to stochastic control and extending neural network approximation results.

Contribution

It establishes a connection between diffusion models and stochastic control, extending neural network approximation results for the Föllmer drift to diffusion models.

Findings

Theoretical guarantees for score matching in diffusion models.

Extension of neural network approximation results.

Insights into the control perspective of diffusion processes.

Abstract

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.