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

TL;DR

GEPC is a training-free method that detects out-of-distribution samples in diffusion models by measuring how the learned score's equivariance properties break under transformations, providing interpretable and competitive results.

Contribution

We introduce GEPC, a novel training-free probe that detects equivariance-breaking in diffusion models for OOD detection, with theoretical bounds and practical interpretability.

Findings

GEPC achieves competitive AUROC on benchmark datasets.

It provides interpretable equivariance-breaking maps.

Effective in high-resolution SAR imagery for anomaly detection.

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/.