Riemannian Diffusion Schrödinger Bridge
This work addresses a bottleneck for researchers and practitioners in fields like climate science by enabling more efficient generative modeling on curved data geometries, though it is incremental as it builds on prior Euclidean and Riemannian methods.
The paper tackles the problem of accelerating sampling and enabling interpolation for diffusion models on Riemannian manifolds, introducing Riemannian Diffusion Schrödinger Bridge, which generalizes existing methods to non-Euclidean settings and shows validation on synthetic and real-world Earth and climate data.
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 \emph{Riemannian Diffusion Schrödinger Bridge}. Our proposed method generalizes Diffusion Schrödinger Bridge introduced in \cite{debortoli2021neurips} 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.