[2604.02751] Understanding Latent Diffusability via Fisher Geometry

Computer Science > Machine Learning arXiv:2604.02751 (cs) [Submitted on 3 Apr 2026] Title:Understanding Latent Diffusability via Fisher Geometry Authors:Jing Gu, Morteza Mardani, Wonjun Lee, Dongmian Zou, Gilad Lerman View a PDF of the paper titled Understanding Latent Diffusability via Fisher Geometry, by Jing Gu and 4 other authors View PDF HTML (experimental) Abstract:Diffusion models often degrade when trained in latent spaces (e.g., VAEs), yet the formal causes remain poorly understood. We quantify latent-space diffusability through the rate of change of the Minimum Mean Squared Error (MMSE) along the diffusion trajectory. Our framework decomposes this MMSE rate into contributions from Fisher Information (FI) and Fisher Information Rate (FIR). We demonstrate that while global isometry ensures FI alignment, FIR is governed by the encoder's local geometric properties. Our analysis explicitly decouples latent geometric distortion into three measurable penalties: dimensional compression, tangential distortion, and curvature injection. We derive theoretical conditions for FIR preservation across spaces, ensuring maintained diffusability. Experiments across diverse autoencoding architectures validate our framework and establish these efficient FI and FIR metrics as a robust diagnostic suite for identifying and mitigating latent diffusion failure. Subjects: Machine Learning (cs.LG) Cite as: arXiv:2604.02751 [cs.LG]   (or arXiv:2604.02751v1 [cs.LG] for this version)   https:/...