论文标题
里曼尼亚扩散schrödinger桥
Riemannian Diffusion Schrödinger Bridge
论文作者
论文摘要
基于得分的生成模型在密度估计和生成建模任务上表现出最先进的性能。这些模型通常假定数据几何形状是平坦的，但已开发出最近的扩展来合成生活在Riemannian歧管上的数据。现有的加速扩散模型采样方法通常不适用于Riemannian设置，基于Riemannian得分的方法尚未适应数据集插值的重要任务。为了克服这些问题，我们介绍了\ emph {Riemannian扩散Schrödinger桥}。我们提出的方法将\ cite {debortoli2021neurips}引入的扩散schrödinger桥概括为非欧几里得设置，并将基于Riemannian得分的模型扩展到首次反转之外。我们验证了有关合成数据以及真实地球和气候数据的建议方法。
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 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.
