Geometric Decoupling: Diagnosing the Structural Instability of Latent

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 Local Scaling (capacity) and Local Complexity (curvature). Our study uncovers a "Geometric Decoupling" : while curvature in normal generation functionally encodes image detail, Out-of-Distribution (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. Our code is at https://github.com/Byronliang8/Diffusion-Geometry.