From Denoising Diffusions to Denoising Markov Models
This work provides a foundational extension for generative modeling, potentially impacting all of ML/AI by broadening the applicability of denoising techniques.
The paper tackles the problem of generalizing denoising diffusion models, which are state-of-the-art generative models, to a wider class of spaces by proposing a unifying framework and an extension of score matching, with results illustrated on various applications.
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.