Geometric Decoupling: Diagnosing the Structural Instability of Latent

2026-04-20

AI Summary

This work addresses the semantic discontinuities that arise during editing in latent diffusion models, which stem from the structural fragility of the latent space. The authors propose a Riemannian geometric framework that decouples the generative Jacobian into local scaling (capacity) and local curvature (complexity). Through this decomposition, they reveal that out-of-distribution generation erroneously allocates curvature to unstable semantic boundaries rather than perceptual details. The study introduces “geometric hotspots” as an intrinsic diagnostic metric to pinpoint the structural origins of generation instability. This approach provides a robust, geometry-aware measure for evaluating and enhancing the reliability of generative models.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

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.

Problem

• Latent Diffusion Models
• Structural Instability
• Latent Space Brittleness
• Semantic Discontinuity
• Geometric Decoupling

Innovation

• Geometric Decoupling
• Latent Diffusion Models
• Riemannian Geometry
• Generative Jacobian
• Geometric Hotspots