Jean Pinsolle

Yadang Alexis Rouzoumka, Jean Pinsolle, Eugénie Terreaux et al.

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/.

Yadang Alexis Rouzoumka, Jean Pinsolle, Eugénie Terreaux et al.

Fair comparison between diffusion-based OOD detectors is challenging, as conclusions can vary with backbone choice, corruption parameterization, and test-time budget. We address this issue through a Mutualized Backbone-Equated (MBE) protocol that aligns canonical corruption levels and logical test-time cost across diffusion backbones. Within this setting, we introduce Canonical Feature Snapshots (CFS), a family of detectors that probes a frozen diffusion backbone using only a tiny number of native internal activations at canonical low-noise levels. On a controlled CIFAR-scale benchmark, the strongest one-forward CFS variant is CFS(1x2), while an even smaller decoder-only variant remains highly competitive. This shows that much of the relative-OOD signal exposed by frozen diffusion backbones is concentrated in a small number of sparse internal states, rather than requiring full denoising trajectories or high-capacity downstream heads. We further provide a local diagnostic theory explaining these observations through conditional encoder-decoder complementarity, diagonal-score separation, and low-noise corruption stability. The official implementation is available at https://github.com/RouzAY/cfs-diffusion-ood/.