Local Diffusion Models and Phases of Data Distributions

Xun Gao investigates when diffusion-model denoisers can exploit the spatial locality of real data. A phase framework identifies distributions connected by local operations. Reverse denoising passes from a trivial phase to a data phase through a rapid transition where purely local denoisers fail. Spatial Markovianity provides a diagnostic tested on real datasets. The results suggest using compact local networks away from the transition and global networks only near it, connecting efficient generative modelling to statistical physics.