Information-Theoretic DiffusionDownload PDF

Published: 01 Feb 2023, Last Modified: 01 Oct 2023ICLR 2023 posterReaders: Everyone
Keywords: diffusion, density models, information theory
TL;DR: A new information-theoretic foundation for diffusion models leads to simpler and more computationally efficient density modeling.
Abstract: Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models inspired by classic results in information theory that connect Information with Minimum Mean Square Error regression, the so-called I-MMSE relations. We generalize the I-MMSE relations to \emph{exactly} relate the data distribution to an optimal denoising regression problem, leading to an elegant refinement of existing diffusion bounds. This new insight leads to several improvements for probability distribution estimation, including a theoretical justification for diffusion model ensembling. Remarkably, our framework shows how continuous and discrete probabilities can be learned with the same regression objective, avoiding domain-specific generative models used in variational methods.
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