From Modes to Memories: Characterizing the Scale-Space Dynamics of Diffusion Models

Excerpt

arXiv:2609.39648v1 Announce Type: new Abstract: Diffusion models are typically viewed as stochastic processes that transform noise into data. We take a complementary perspective: a diffusion model defines a family of deterministic dynamical systems indexed by noise scale. At each fixed scale $\sigma$, we treat the denoiser as a self-map and study its dynamics. For an exact denoiser, fixed points correspond to critical points of the smoothed data density, while attractors correspond to its modes;