Riemannian Diffusion Schrödinger Bridge
Riemannian Diffusion Schrödinger Bridge
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DOI：
10.48550/arxiv.2207.03024
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
James Thornton;M. Hutchinson;Emile Mathieu;Valentin De Bortoli;Yee Whye Teh;A. Doucet
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文献类型：
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作者：
James Thornton;M. Hutchinson;Emile Mathieu;Valentin De Bortoli;Yee Whye Teh;A. Doucet
基于分数的产生式模型在密度估计和产生式建模任务中表现出最先进的性能。这些模型通常假设数据几何是平坦的，然而最近已经开发出扩展来合成生活在黎曼流形上的数据。现有的加速采样扩散模型的方法通常不适用于黎曼环境，而基于黎曼分数的方法尚未适应数据集的内插这一重要任务。为了克服这些问题，我们引入了Riemannian扩散Schr odinger桥，我们所提出的方法将{debortoli2021nerips}中引入的扩散Schr odinger桥推广到非欧几里德环境，并将基于黎曼分数的模型推广到第一次可逆的情形。我们在合成数据和真实的地球和气候数据上验证了我们提出的方法。
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 Schr\"odinger Bridge}. Our proposed method generalizes Diffusion Schr\"odinger 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.