Geometric Decoupling: Diagnosing the Structural Instability of Latent
For researchers and practitioners using latent diffusion models, this work provides an intrinsic metric to diagnose generative reliability, addressing the problem of discontinuous semantic jumps during editing.
The paper diagnoses the structural instability of latent diffusion models by introducing a Riemannian framework that decomposes latent geometry into local scaling and curvature, revealing a 'Geometric Decoupling' where out-of-distribution generation misallocates curvature to unstable semantic boundaries rather than perceptible details.
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.