A real Stable Diffusion 1.5 latent space shows a fractal structure of Fisher-metric phase transitions, with diverging Lipschitz constants at phase boundaries

A Fisher information metric is reconstructed from a log-partition-function formulation of the latent space of a real Stable Diffusion 1.5 (Dreamshaper8 checkpoint) model, after first validating the reconstruction method against the exactly-solvable 2D Ising model and TASEP [lobashev-etal-2026-hessian-geometry-latent-space-generative-models] The real diffusion model's latent space shows a fractal structure of phase transitions, marked by abrupt jumps in the Fisher metric rather than smooth curvature variation [lobashev-etal-2026-hessian-geometry-latent-space-generative-models] Geodesic interpolation is locally linear within a single phase, but this breaks down at phase boundaries, where the local Lipschitz constant diverges [lobashev-etal-2026-hessian-geometry-latent-space-generative-models]