Irregularities of Latent Space Geometry in Diffusion Models

This paper extends experimental evidence of high- Lipschitz irregularities in diffusion mappings from the prior distribution to the data distribu- tion. Previously, it was observed that for diffusion models, slight variation of the initial Gaussian noise results in notably different generated im- ages. This behavior has been associated with mode coverage of diffusion mapping and high local Lipschitz constants. We quantify local ge- ometry on two-dimensional latent slices using the pullback metric $G= J^\top J$ of a perceptual fea- ture map; its determinant statistic $S=\sqrt{\det{G}}$ measures local area expansion, while the operator norm ∥J∥op gives the local slice Lipschitz mod- ulus. Previous experiments in the literature were limited to one architecture, namely Stable Diffu- sion 1.5. The presented work examines a wider range of models and architectures and discusses the effect of distillation and few-step generation in Wan 2.1, FLUX Klein distill, and Z-Image Turbo. Additionally, we present an analysis of the inter- nal state of DiT during denoising to determine specific layers contributing to the high Lipschitz constant of a total mapping