GPFlow: Gaussian Prototype Probability Flow for Unsupervised Multi-Modal Anomaly Detection

In this paper, we study unsupervised multi-modal anomaly detection under challenging few-shot conditions, where only a few normal training samples are available for each class. To prevent the trivial reconstruction of anomalies, recent methods often rely on discrete prototypes to establish an information bottleneck. However, such discrete prototypes fail to capture continuous and anisotropic variations of normal features. We therefore propose GPFlow, a probability-flow-inspired framework that models normality using learnable Gaussian prototypes. The key component of GPFlow is an analytical Posterior-Mean Path (PMP) router, which reconstructs features through the posterior mean of a noise-smoothed Gaussian mixture. This yields anisotropic shrinkage as a covariance-aware information bottleneck: PMP selectively preserves normal variations aligned with the covariance structure of Gaussian prototypes while strictly suppressing deviations inconsistent with the prototypes. To exploit complementary knowledge across modalities, GPFlow further combines intra-modal and cross-modal reconstruction, and applies a lightweight instance-aware prior calibration to alleviate the distribution mismatch between sparse training data and diverse test samples. Experiments on MVTec-3D-AD and Eyecandies show that GPFlow achieves significant performance improvement with only a few normal training samples while remaining computationally efficient.