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/.

翻译：扩散模型学习一个时间索引的得分场$\mathbf{s}_θ(\mathbf{x}_t,t)$，该得分场通常从分布内数据及卷积骨干网络中继承近似等变性（翻转、旋转、循环平移）。大多数基于扩散的分布外检测器利用得分幅度或局部几何特性（能量、曲率、协方差谱），而很大程度上忽略了等变性。我们提出了群等变后验一致性，这是一种无需训练的探针方法，用于衡量学习到的得分在有限群$\mathcal{G}$作用下的变换一致性，即使在得分幅度保持不变时也能检测到等变性破缺。在总体水平上，我们提出了理想的GEPC残差，该残差将等变残差泛函在$\mathcal{G}$上取平均，并在温和假设下推导了分布内上界和分布外下界。GEPC仅需进行得分评估，并能生成可解释的等变性破缺图。在分布外图像基准数据集上，我们证明GEPC相较于近期基于扩散的基线方法，在保持计算轻量化的同时，取得了具有竞争力或更优的AUROC性能。在高分辨率合成孔径雷达图像中，其中分布外对应杂波中的目标或异常，GEPC实现了强大的目标-背景分离能力，并生成了视觉上可解释的等变性破缺图。代码可在https://github.com/RouzAY/gepc-diffusion/获取。