Riemannian Diffusion Schrödinger Bridge
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by
James Thornton, Michael Hutchinson, Emile Mathieu, Valentin De Bortoli, Yee Whye Teh, Arnaud Doucet
2022
Abstract
Score-based generative models exhibit state of the art performance on density
estimation and generative modeling tasks. These models typically assume that
the data geometry is flat, yet recent extensions have been developed to
synthesize data living on Riemannian manifolds. Existing methods to accelerate
sampling of diffusion models are typically not applicable in the Riemannian
setting and Riemannian score-based methods have not yet been adapted to the
important task of interpolation of datasets. To overcome these issues, we
introduce Riemannian Diffusion Schrödinger Bridge. Our proposed method
generalizes Diffusion Schrödinger Bridge introduced in
<cit.> to the non-Euclidean setting and extends Riemannian
score-based models beyond the first time reversal. We validate our proposed
method on synthetic data and real Earth and climate data.
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2207.03024v1
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