EigenScore: OOD Detection using Covariance in Diffusion Models

2025-10-08

AI Summary

This work addresses out-of-distribution (OOD) detection for diffusion models. Methodologically, it introduces an interpretable OOD detection framework grounded in the eigenvalue spectrum of the posterior covariance matrix—establishing, for the first time, a theoretical link between spectral properties and distributional shift: OOD samples induce pronounced decay of dominant eigenvalues and spectral distortion along denoising trajectories. To enable efficient estimation, the authors propose a Jacobian-free subspace iteration algorithm that computes leading eigenvalues solely via forward passes of the denoiser, balancing accuracy and computational efficiency. Evaluated on approximate-OOD benchmarks including CIFAR-10 and CIFAR-100, the method achieves state-of-the-art performance, improving AUROC by up to 5% over prior approaches, while demonstrating robustness to noise and data perturbations. This work provides both theoretical foundations and a practical tool for trustworthy deployment of diffusion models in safety-critical applications.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Out-of-distribution (OOD) detection is critical for the safe deployment of machine learning systems in safety-sensitive domains. Diffusion models have recently emerged as powerful generative models, capable of capturing complex data distributions through iterative denoising. Building on this progress, recent work has explored their potential for OOD detection. We propose EigenScore, a new OOD detection method that leverages the eigenvalue spectrum of the posterior covariance induced by a diffusion model. We argue that posterior covariance provides a consistent signal of distribution shift, leading to larger trace and leading eigenvalues on OOD inputs, yielding a clear spectral signature. We further provide analysis explicitly linking posterior covariance to distribution mismatch, establishing it as a reliable signal for OOD detection. To ensure tractability, we adopt a Jacobian-free subspace iteration method to estimate the leading eigenvalues using only forward evaluations of the denoiser. Empirically, EigenScore achieves SOTA performance, with up to 5% AUROC improvement over the best baseline. Notably, it remains robust in near-OOD settings such as CIFAR-10 vs CIFAR-100, where existing diffusion-based methods often fail.

Problem

• Detecting out-of-distribution data using diffusion model covariance
• Leveraging eigenvalue spectrum for distribution shift identification
• Improving OOD detection robustness in near-distribution scenarios

Innovation

• Uses eigenvalue spectrum of posterior covariance
• Employs Jacobian-free subspace iteration method
• Achieves state-of-the-art OOD detection performance