Riemannian Score-Based Generative Modeling

• URL: http://arxiv.org/abs/2202.02763v1
• Date: Sun, 6 Feb 2022 11:57:39 GMT
• Title: Riemannian Score-Based Generative Modeling
• Authors: Valentin De Bortoli, Emile Mathieu, Michael Hutchinson, James Thornton, Yee Whye Teh, Arnaud Doucet
• Abstract summary: We introduce score-based generative models (SGMs) demonstrating remarkable empirical performance. Current SGMs make the underlying assumption that the data is supported on a Euclidean manifold with flat geometry. This prevents the use of these models for applications in robotics, geoscience or protein modeling.
• Score: 56.20669989459281
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Score-based generative models (SGMs) are a novel class of generative models demonstrating remarkable empirical performance. One uses a diffusion to add progressively Gaussian noise to the data, while the generative model is a "denoising" process obtained by approximating the time-reversal of this "noising" diffusion. However, current SGMs make the underlying assumption that the data is supported on a Euclidean manifold with flat geometry. This prevents the use of these models for applications in robotics, geoscience or protein modeling which rely on distributions defined on Riemannian manifolds. To overcome this issue, we introduce Riemannian Score-based Generative Models (RSGMs) which extend current SGMs to the setting of compact Riemannian manifolds. We illustrate our approach with earth and climate science data and show how RSGMs can be accelerated by solving a Schr\"odinger bridge problem on manifolds.

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