GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models
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arXiv
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| Format: | Preprint |
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2026
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| author | Rouzoumka, Yadang Alexis Pinsolle, Jean Terreaux, Eugénie Morisseau, Christèle Ovarlez, Jean-Philippe Ren, Chengfang |
| author_facet | Rouzoumka, Yadang Alexis Pinsolle, Jean Terreaux, Eugénie Morisseau, Christèle Ovarlez, Jean-Philippe Ren, Chengfang |
| contents | 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/. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00191 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models Rouzoumka, Yadang Alexis Pinsolle, Jean Terreaux, Eugénie Morisseau, Christèle Ovarlez, Jean-Philippe Ren, Chengfang Machine Learning Computer Vision and Pattern Recognition 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/. |
| title | GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2602.00191 |