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

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 $G$, 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 $G$, 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. The official implementation is available at https://github.com/RouzAY/gepc-diffusion/.

Modern AI systems can make confident mistakes when they receive inputs that are different from the data they were designed for. This paper proposes a way to detect such unusual inputs using diffusion models. The key idea is to check whether the model behaves consistently when an image is transformed, for example by flipping, rotating, or shifting it. For normal inputs, the model's internal predictions should transform in a consistent way; for unusual inputs, this consistency can break. Our method, GEPC, measures this breaking of consistency without retraining the model. It produces both a numerical anomaly score and visual maps showing where the inconsistency appears in the image. We evaluate the method on image benchmarks and on radar imagery, where the maps can highlight ships or wakes in cluttered scenes.