Geometric Decoupling: Diagnosing the Structural Instability of Latent
Yuanbang Liang, Zhengwen Chen, Yu-Kun Lai
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 *Local Scaling* (capacity) and *Local Complexity* (curvature). Our study uncovers a **``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.
BibTeX
@inproceedings{
liang2026geometric,
title={Geometric Decoupling: Diagnosing the Structural Instability of Latent},
author={Yuanbang Liang and Zhengwen Chen and Yu-Kun Lai},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=QXgHl2nTEX}
}