Multi-Scale Denoising Score Matching
An interactive live film: solving the manifold problem via a geometric noise ladder; large noise blankets empty space with global guidance, while small noise resolves fine modes during reverse diffusion.
Narration
Data in the real world concentrates on low-dimensional manifolds. In empty regions far from any data points, there is almost nothing to learn the score from, so its estimate is unreliable.
Look at these two separated data clusters. Between them lies vast empty space where probabilities are nearly zero. A single score model trained only on clean data gets lost here.
The rest of the narration is in the book's Companion.
