Riemannian score-based generative modelling
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, wh...
| Main Authors: | , , , , , |
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| Format: | Conference item |
| Language: | English |
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Curran Associates
2023
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| _version_ | 1826311184882597888 |
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| author | De Bortoli, V Mathieu, E Hutchinson, M Thornton, J Teh, YW Doucet, A |
| author_facet | De Bortoli, V Mathieu, E Hutchinson, M Thornton, J Teh, YW Doucet, A |
| author_sort | De Bortoli, V |
| collection | OXFORD |
| description | 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.
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| first_indexed | 2024-03-07T08:04:36Z |
| format | Conference item |
| id | oxford-uuid:17323cf8-d8e6-405c-abf9-a33e6bf752d6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:04:36Z |
| publishDate | 2023 |
| publisher | Curran Associates |
| record_format | dspace |
| spelling | oxford-uuid:17323cf8-d8e6-405c-abf9-a33e6bf752d62023-10-30T09:49:51ZRiemannian score-based generative modellingConference itemhttp://purl.org/coar/resource_type/c_5794uuid:17323cf8-d8e6-405c-abf9-a33e6bf752d6EnglishSymplectic ElementsCurran Associates2023De Bortoli, VMathieu, EHutchinson, MThornton, JTeh, YWDoucet, AScore-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. |
| spellingShingle | De Bortoli, V Mathieu, E Hutchinson, M Thornton, J Teh, YW Doucet, A Riemannian score-based generative modelling |
| title | Riemannian score-based generative modelling |
| title_full | Riemannian score-based generative modelling |
| title_fullStr | Riemannian score-based generative modelling |
| title_full_unstemmed | Riemannian score-based generative modelling |
| title_short | Riemannian score-based generative modelling |
| title_sort | riemannian score based generative modelling |
| work_keys_str_mv | AT debortoliv riemannianscorebasedgenerativemodelling AT mathieue riemannianscorebasedgenerativemodelling AT hutchinsonm riemannianscorebasedgenerativemodelling AT thorntonj riemannianscorebasedgenerativemodelling AT tehyw riemannianscorebasedgenerativemodelling AT douceta riemannianscorebasedgenerativemodelling |