Geometric Decoupling: Diagnosing the Structural Instability of Latent

• URL: http://arxiv.org/abs/2604.18804v1
• Date: Mon, 20 Apr 2026 20:22:27 GMT
• Title: Geometric Decoupling: Diagnosing the Structural Instability of Latent
• Abstract summary: We analyze the generative Jacobian, decomposing geometry into textitLocalScaling (capacity) and textitLocal Complexity (curvature)<n>Our study uncovers a textbfGeometric 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.
• Score: 44.374154158781295
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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