GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models
This addresses the challenge of detecting anomalies or novel data for applications like image analysis and radar target detection, representing an incremental improvement over existing diffusion-based methods.
The paper tackles the problem of out-of-distribution detection in diffusion models by introducing GEPC, a method that measures score equivariance consistency, achieving competitive or improved AUROC on benchmark datasets and strong target-background separation in radar imagery.
Diffusion models learn a time-indexed score field $\mathbf{s}_θ(\mathbf{x}_t,t)$ 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/.