How and Why: Taming Flow Matching for Unsupervised Anomaly Detection and Localization

Abstract: We propose a new paradigm for unsupervised anomaly detection and localization using Flow Matching (FM), which fundamentally addresses the model expressivity limitations of conventional flow-based methods. To this end, we formalize the concept of time-reversed Flow Matching (rFM) as a vector field regression along a predefined probability path to transform unknown data distributions into standard Gaussian. We bring two core observations that reshape our understanding of FM. First, we rigorously prove that FM with linear interpolation probability paths is inherently non-invertible. Second, our analysis reveals that employing reversed Gaussian probability paths in high-dimensional spaces can lead to trivial vector fields. This issue arises due to the manifold-related constraints. Building on the second observation, we propose Worst Transport (WT) displacement interpolation to reconstruct a non-probabilistic evolution path. The proposed WT-Flow enhances dynamical control over sample trajectories, constructing ''degenerate potential wells'' for anomaly-free samples while allowing anomalous samples to escape. This novel unsupervised paradigm offers a theoretically grounded separation mechanism for anomalous samples. Notably, FM provides a computationally tractable framework that scales to complex data. We present the first successful application of FM for the unsupervised anomaly detection task, achieving state-of-the-art performance at a single scale on the MVTec dataset. The reproducible code for training will be released upon camera-ready submission.