From denoising diffusions to denoising Markov models
Joe Benton, Yuyang Shi, Valentin De Bortoli, George Deligiannidis, Arnaud Doucet
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2024 · Volume 86 · Issue 2
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 generalizing 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.
Keywords
denoising diffusions, generative models, posterior simulation, score matching, unifying framework
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