Geometric Decoupling: Diagnosing the Structural Instability of Latent

Yuanbang Liang, Zhengwen Chen, Yu-Kun Lai
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:73069-73091, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-liang26d, title = {Geometric Decoupling: Diagnosing the Structural Instability of Latent}, author = {Liang, Yuanbang and Chen, Zhengwen and Lai, Yu-Kun}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {73069--73091}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/liang26d/liang26d.pdf}, url = {https://proceedings.mlr.press/v306/liang26d.html}, 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.} }
Endnote
%0 Conference Paper %T Geometric Decoupling: Diagnosing the Structural Instability of Latent %A Yuanbang Liang %A Zhengwen Chen %A Yu-Kun Lai %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-liang26d %I PMLR %P 73069--73091 %U https://proceedings.mlr.press/v306/liang26d.html %V 306 %X 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.
APA
Liang, Y., Chen, Z. & Lai, Y.. (2026). Geometric Decoupling: Diagnosing the Structural Instability of Latent. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:73069-73091 Available from https://proceedings.mlr.press/v306/liang26d.html.

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