From Denoising Diffusions to Denoising Markov Models

TL;DR

This paper introduces a unifying framework that extends denoising diffusion models and score matching to a broader class of spaces, enhancing their applicability in generative modeling and posterior simulation.

Contribution

It generalizes denoising diffusion and score matching techniques to new spaces, providing a novel extension and unification of these methods.

Findings

Effective in various applications

Generalizes to new spaces

Improves generative modeling capabilities

Abstract

Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain synthetic datapoints. The denoising diffusion relies on approximations of the logarithmic derivatives of the noised data densities using score matching. Such models can also be used to perform approximate posterior simulation when one can only sample from the prior and likelihood. We propose a unifying framework generalising this approach to a wide class of spaces and leading to an original extension of score matching. We illustrate the resulting models on various applications.