Understanding Latent Diffusability via Fisher Geometry

תקציר מקורי באנגליתarXiv:2604.02751v3 Announce Type: replace Abstract: Diffusion models often degrade in latent spaces, yet the formal causes remain poorly understood. We quantify latent-space diffusability via 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 show that isometric embeddings preserve intrinsic FI and establish quantitative intrinsic-FI bounds for a broader class of bi-Lipschitz encoders with controlled weak volume distortion, whereas FIR is governed by the interplay between encoder and data geometries. Our analysis separates four geometric contributions in local stability bounds for Gaussian-smoothed FIR: dimensional compressio