Geometric decoupling: diagnosing the structural instability of latent

Liang, Yuanbang, Chen, Zhengwen and Lai, Yu Kun ORCID: https://orcid.org/0000-0002-2094-5680 2026. Geometric decoupling: diagnosing the structural instability of latent. Presented at: 43rd International Conference on Machine Learning, Seoul, South Korea, 6-11 July 2026. Proceedings of the 43rd International Conference on Machine Learning. Proceedings of Machine Learning Research , vol.306 PMLR, pp. 73069-73091. Item availability restricted.

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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, 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.

Item Type:	Conference or Workshop Item - unpublished
Status:	Unpublished
Schools:	Schools > Computer Science & Informatics
Publisher:	PMLR
Funders:	EPSRC
Projects:	EP/Y028805/1
Date of First Compliant Deposit:	1 July 2026
Date of Acceptance:	30 April 2026
Last Modified:	03 Nov 2026 16:00
URI:	https://orca.cardiff.ac.uk/id/eprint/187865

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