Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balance

Haiqi Lu, Ying Tang

Keywords: diffusion models, memorization, generalization, dynamical regimes, speciation, collapse, non-reversible dynamics

TL;DR: We show that non-reversible diffusion dynamics can shift speciation and collapse regimes in diffusion models, with geometry-aware currents advancing speciation more reliably than collapse.

Abstract: Diffusion models pass through time-localized dynamical regimes in which samples first commit to semantic modes and may later collapse toward individual training examples. We study how these regimes change when the forward Ornstein--Uhlenbeck noising process is made non-reversible while preserving its invariant Gaussian measure. The drift is written as $\mathbf{A}=(\mathbf{I}+\mathbf{Q})\mathbf{U}$, where $\mathbf{U}$ fixes the stationary geometry and the anti-symmetric matrix $\mathbf{Q}$ creates probability currents. We derive a matrix criterion for the speciation time and a Random-Energy-Model criterion for collapse that depends on a Mahalanobis signal-to-noise spectrum. Experiments on Gaussian mixtures and trained DDPMs show that geometry-aware non-reversibility can move speciation earlier, whereas collapse timing is not generically moved earlier by breaking detailed balance.

Submission Number: 110