在图像扩散隐空间中计算概率密度测地线，实现无需训练的图像序列插值与外推。
Probability Density Geodesics in Image Diffusion Latent Space
- 基于空间可变内积定义概率密度相关的测地线路径。
- 高概率区域路径更短，能准确计算两点间测地距离。
- 适用于预训练模型的图像序列插值与外推，无需重新训练。
扩散模型间接估计数据空间上的概率密度，可用于研究其结构。本文表明可在扩散隐空间中计算测地线，其中由空间可变内积诱导的范数与概率密度成反比。在此设定下，穿越高密度（即高概率）图像隐空间区域的路径比经过低密度区域的等效路径更短。我们提出了求解相关初值与边值问题的算法，并展示了如何沿路径计算概率密度及两点间的测地距离。利用这些技术，我们分析了视频片段在预训练图像扩散空间中逼近测地线的程度。最后，我们演示了这些方法如何应用于基于预训练图像扩散模型的训练自由图像序列插值与外推。
原文摘要 · Abstract (English)
Diffusion models indirectly estimate the probability density over a data space, which can be used to study its structure. In this work, we show that geodesics can be computed in diffusion latent space, where the norm induced by the spatially-varying inner product is inversely proportional to the probability density. In this formulation, a path that traverses a high density (that is, probable) region of image latent space is shorter than the equivalent path through a low density region. We present algorithms for solving the associated initial and boundary value problems and show how to compute the probability density along the path and the geodesic distance between two points. Using these techniques, we analyze how closely video clips approximate geodesics in a pre-trained image diffusion space. Finally, we demonstrate how these techniques can be applied to training-free image sequence interpolation and extrapolation, given a pre-trained image diffusion model.
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