Riemannian score-based generative modelling

Conference item

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 adenoising'' 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.

Authors: De Bortoli, V; Mathieu, E; Hutchinson, M; Thornton, J; Teh, YW

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Curran Associates
• Host title: Advances in Neural Information Processing Systems 35 (NeurIPS 2022)
• Volume: 4
• Pages: 2406-2422
• Publication date: 2023-04-01
• Acceptance date: 2022-09-14
• Event title: 36th Annual Conference on Neural Information Processing Systems (NeurIPS 2022)
• Event location: New Orleans, USA
• Event website: https://nips.cc/Conferences/2022
• Event start date: 2022-11-11
• Event end date: 2022-12-09
• ISSN: 1049-5258
• EISBN: 9781713873129
• ISBN: 9781713871088
• Language: English
• Keywords: FFR