Denoising Diffusions with Optimal Transport: Localization, Curvature, and Multi-Scale Complexity
Adding noise is easy; what about denoising? Diffusion is easy; what about reverting a diffusion? We provide a fine-grained analysis of the diffuse-then-denoise process. We discover a notion of multi-scale curvature complexity that collectively determines the success or failure mode of probabilistic diffusion models.