论文标题
基于Riemannian得分的生成建模
Riemannian Score-Based Generative Modelling
论文作者
论文摘要
基于得分的生成模型（SGM）是一类强大的生成模型，具有出色的经验性能。基于得分的生成建模（SGM）由``noising''阶段组成，从而将扩散逐渐将高斯噪声添加到数据中，而生成模型则需要通过近似扩散的时间交换时间来定义的``deNoisising''过程。现有的SGMS假定在欧几里得空间上支持数据，即具有平坦几何形状的歧管。在机器人技术，地球科学或蛋白质建模等许多领域中，数据通常由生活在riemannian歧管上的分布和当前的SGM技术自然描述。我们在这里介绍了基于Riemannian得分的生成模型（RSGMS），这是一种将SGM扩展到Riemannian歧管的生成模型。我们展示了我们在各种歧管上，尤其是地球和气候科学球形数据的方法。
Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a ``denoising'' process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.
