揭示扩散模型潜在空间不稳定的几何根源，提出诊断新方法。
Geometric Decoupling: Diagnosing the Structural Instability of Latent
- 用黎曼几何分析生成雅可比矩阵，分解出局部缩放与复杂度。
- 发现异常生成时曲率被浪费在不稳定的语义边界而非细节上。
- 定位几何热点，为生成可靠性提供内在评估指标，适合模型开发者。
潜在扩散模型（LDMs）虽能实现高保真生成，但其潜在空间存在脆性问题，导致编辑时出现语义跳跃。本文引入黎曼框架，通过分析生成雅可比矩阵，将几何特性分解为局部缩放（容量）与局部复杂度（曲率）。研究揭示了一种‘几何解耦’现象：正常生成中曲率功能上编码图像细节，而分布外（OOD）生成时则出现功能解耦，极端曲率被浪费于不稳定的语义边界而非可感知细节。这一几何错配识别出‘几何热点’作为不稳定的结构根源，提供了一种鲁棒的内在指标，用于诊断生成可靠性。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。