论文标题
黎曼扩散模型
Riemannian Diffusion Models
论文作者
论文摘要
扩散模型是图像产生和可能性估计的最新方法。在这项工作中，我们将连续的时间扩散模型推广到任意的Riemannian流形，并得出了可能性估计的变异框架。在计算上，我们提出了计算可能性估计中需要的新方法。此外，在概括欧几里得案例时，我们证明，最大化这种变分的下限等效于Riemannian得分匹配。从经验上讲，我们在各种光滑的歧管上（例如球，托里，双曲线和正交基团）展示了里曼尼亚扩散模型的表达能力。我们提出的方法在所有基准测试基准上实现了新的最先进的可能性。
Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for likelihood estimation. Computationally, we propose new methods for computing the Riemannian divergence which is needed in the likelihood estimation. Moreover, in generalizing the Euclidean case, we prove that maximizing this variational lower-bound is equivalent to Riemannian score matching. Empirically, we demonstrate the expressive power of Riemannian diffusion models on a wide spectrum of smooth manifolds, such as spheres, tori, hyperboloids, and orthogonal groups. Our proposed method achieves new state-of-the-art likelihoods on all benchmarks.
