Geometric Decoupling: Diagnosing the Structural Instability of Latent

TL;DR

This paper introduces a Riemannian framework to diagnose and understand the structural instability of Latent Diffusion Models by analyzing their geometric properties, revealing the root causes of brittleness.

Contribution

It proposes a novel geometric decoupling analysis that identifies hotspots of instability in latent space, offering a new intrinsic metric for generative reliability.

Findings

Normal generation curvature encodes image detail

OOD generation shows decoupling where curvature is wasted on unstable boundaries

Identifies geometric hotspots as the root of instability

Abstract

Latent Diffusion Models (LDMs) achieve high-fidelity synthesis but suffer from latent space brittleness, causing discontinuous semantic jumps during editing. We introduce a Riemannian framework to diagnose this instability by analyzing the generative Jacobian, decomposing geometry into \textit{Local Scaling} (capacity) and \textit{Local Complexity} (curvature). Our study uncovers a \textbf{``Geometric Decoupling"}: while curvature in normal generation functionally encodes image detail, OOD generation exhibits a functional decoupling where extreme curvature is wasted on unstable semantic boundaries rather than perceptible details. This geometric misallocation identifies ``Geometric Hotspots" as the structural root of instability, providing a robust intrinsic metric for diagnosing generative reliability.