Time-reversed Flow Matching with Worst Transport in High-dimensional Latent Space for Image Anomaly Detection

TL;DR

This paper introduces WT-Flow, a novel flow matching method for image anomaly detection that addresses theoretical and computational challenges of existing models, achieving state-of-the-art results with fast inference.

Contribution

It proposes time-reversed Flow Matching with Worst Transport, overcoming singularity and high-dimensional irregularities, and demonstrates superior performance and efficiency in image anomaly detection.

Findings

WT-Flow achieves state-of-the-art results among single-scale flow methods.

The method enables real-time inference with only 6.7 ms per image.

Experiments on five datasets validate the effectiveness of WT-Flow.

Abstract

Likelihood-based deep generative models have been widely investigated for Image Anomaly Detection (IAD), particularly Normalizing Flows, yet their strict architectural invertibility needs often constrain scalability, particularly in large-scale data regimes. Although time-parameterized Flow Matching (FM) serves as a scalable alternative, it remains computationally challenging in IAD due to the prohibitive costs of Jacobian-trace estimation. This paper proposes time-reversed Flow Matching (rFM), which shifts the objective from exact likelihood computation to evaluating target-domain regularity through density proxy estimation. We uncover two fundamental theoretical bottlenecks in this paradigm: first, the reversed vector field exhibits a non-Lipschitz singularity at the initial temporal boundary, precipitating explosive estimation errors. Second, the concentration of measure in high-dimensional Gaussian manifolds induces structured irregularities, giving rise to a Centripetal Potential Field (CPF) that steers trajectories away from Optimal Transport (OT) paths. We identify these observations as the inherent dualities between FM and rFM. To address these issues, we introduce local Worst Transport Flow matching (WT-Flow), which amplifies the observed CPF of rFM to mitigate the initial singularity while circumventing the need for exact distribution transformations via density proxy. Experiments on five datasets demonstrate that WT-Flow achieves state-of-the-art performance among single-scale flow-based methods, and competitive performance against leading multi-scale approaches. Furthermore, the proposed framework enables superior one-step inference, achieving a per-image flow latency of only 6.7 ms. Our code is available on https://github.com/lil-wayne-0319/fmad.