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

2025-08-07

AI Summary

To address the limited representational capacity of conventional flow models in unsupervised anomaly detection and localization, this paper proposes Worst Transport-Flow (WT-Flow): a novel framework built upon Flow Matching (FM) that constructs a time-reversed vector field to expose the irreversibility of linear interpolation paths and Gaussian degeneration in high dimensions. WT-Flow introduces Worst Transport displacement interpolation—establishing a non-probabilistic evolution path—and constructs a “degeneration potential well” in latent space to effectively separate normal from anomalous samples. Crucially, it provides the first theoretical characterization of FM’s separability mechanism for anomaly detection, thereby decoupling performance from strict distribution reversibility assumptions inherent in standard flow models. Evaluated on the MVTec AD dataset, WT-Flow achieves state-of-the-art performance using a single-scale architecture. This work establishes the first scalable and interpretable FM-based paradigm for unsupervised anomaly detection.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Addressing expressivity limits in flow-based anomaly detection
• Solving non-invertibility in linear Flow Matching paths
• Preventing trivial vector fields in high-dimensional spaces

Innovation

• Time-reversed Flow Matching for Gaussian transformation
• Worst Transport for non-probabilistic path reconstruction
• Degenerate potential wells for anomaly separation