GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models

2026-01-30

AI Summary

Existing diffusion-based out-of-distribution (OOD) detection methods primarily rely on score magnitude or local geometric features, often overlooking the inherent group equivariances—such as rotation and reflection—present in both data and models, thereby failing to detect OOD samples that violate these symmetries. This work proposes GEPC, a training-free method that, for the first time, incorporates group equivariant consistency into diffusion-based OOD detection by evaluating the transformation consistency of the score field under finite group actions. GEPC effectively identifies OOD inputs even when score magnitudes remain unchanged. We define an ideal GEPC residual, establish its theoretical upper and lower bounds, and generate interpretable equivariance violation maps. Experiments demonstrate that GEPC achieves or surpasses state-of-the-art diffusion-based baselines in AUROC on standard image benchmarks and excels in target-background separation and visual interpretability on high-resolution synthetic aperture radar imagery.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Diffusion models learn a time-indexed score field $\mathbf{s}_\theta(\mathbf{x}_t,t)$ that often inherits approximate equivariances (flips, rotations, circular shifts) from in-distribution (ID) data and convolutional backbones. Most diffusion-based out-of-distribution (OOD) detectors exploit score magnitude or local geometry (energies, curvature, covariance spectra) and largely ignore equivariances. We introduce Group-Equivariant Posterior Consistency (GEPC), a training-free probe that measures how consistently the learned score transforms under a finite group $\mathcal{G}$, detecting equivariance breaking even when score magnitude remains unchanged. At the population level, we propose the ideal GEPC residual, which averages an equivariance-residual functional over $\mathcal{G}$, and we derive ID upper bounds and OOD lower bounds under mild assumptions. GEPC requires only score evaluations and produces interpretable equivariance-breaking maps. On OOD image benchmark datasets, we show that GEPC achieves competitive or improved AUROC compared to recent diffusion-based baselines while remaining computationally lightweight. On high-resolution synthetic aperture radar imagery where OOD corresponds to targets or anomalies in clutter, GEPC yields strong target-background separation and visually interpretable equivariance-breaking maps. Code is available at https://github.com/RouzAY/gepc-diffusion/.

Problem

• out-of-distribution detection
• diffusion models
• group equivariance
• score-based models
• anomaly detection

Innovation

• Group Equivariance
• Out-of-Distribution Detection
• Diffusion Models
• Score Function
• Equivariance Breaking