Riemannian Score-Based Generative ModellingDownload PDF

Published: 31 Oct 2022, Last Modified: 11 Jan 2023NeurIPS 2022 AcceptReaders: Everyone
Keywords: Diffusion models, generative modeling, Riemannian manifolds, score matching
TL;DR: Denosing diffusion models on compact Riemannian manifolds for generative modeling
Abstract: Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a ``denoising'' process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here \emph{Riemannian Score-based Generative Models} (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of compact manifolds, and in particular with earth and climate science spherical data.
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