From Modes to Memories: Characterizing the Scale-Space Dynamics of Diffusion Models
The paper interprets diffusion models as dynamical systems indexed by noise scale, using a critical scale ($\sigma_c$) to measure how long an example remains an attractor under denoiser iteration. This scale quantifies memorization, distinguishing between duplication and outliers. It provides a framework to characterize how models memorize data based on the probability mass and spatial location of the examples.