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

• URL: http://arxiv.org/abs/2508.05461v1
• Date: Thu, 07 Aug 2025 15:02:07 GMT
• Title: How and Why: Taming Flow Matching for Unsupervised Anomaly Detection and Localization
• Authors: Liangwei Li, Lin Liu, Juanxiu Liu, Jing Zhang, Ruqian Hao, Xiaohui Du,
• Abstract summary: We formalize the concept of time-reversed Flow Matching as a vector field regression.<n>We show that FM with linear probability paths is inherently non-invertible.<n>We present the first successful application of FM for the unsupervised anomaly detection task.
• Score: 15.283777345273089
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Strengthening Anomaly Awareness [0.0]
  We present a refined version of the Anomaly Awareness framework for enhancing unsupervised anomaly detection.<n>Our approach introduces minimal supervision into Variational Autoencoders (VAEs) through a two-stage training strategy.
  arXiv  Detail & Related papers  (2025-04-15T16:52:22Z)
• On the Wasserstein Convergence and Straightness of Rectified Flow [54.580605276017096]
  Rectified Flow (RF) is a generative model that aims to learn straight flow trajectories from noise to data.<n>We provide a theoretical analysis of the Wasserstein distance between the sampling distribution of RF and the target distribution.<n>We present general conditions guaranteeing uniqueness and straightness of 1-RF, which is in line with previous empirical findings.
  arXiv  Detail & Related papers  (2024-10-19T02:36:11Z)
• DFM: Interpolant-free Dual Flow Matching [0.8192907805418583]
  We propose an interpolant-free dual flow matching (DFM) approach without explicit assumptions about the modeled vector field. Experiments with the SMAP unsupervised anomaly detection show advantages of DFM when compared to the CNF trained with either maximum likelihood or FM objectives.
  arXiv  Detail & Related papers  (2024-10-11T20:46:04Z)
• Stream-level flow matching with Gaussian processes [4.935875591615496]
  Conditional flow matching (CFM) is a family of training algorithms for fitting continuous normalizing flows (CNFs)<n>We extend the CFM algorithm by defining conditional probability paths along streams'', instances of latent paths that connect data pairs of source and target.<n>We show that this generalization of the CFM can effectively reduce the variance in the estimated marginal vector field at a moderate computational cost.
  arXiv  Detail & Related papers  (2024-09-30T15:47:22Z)
• GLAD: Towards Better Reconstruction with Global and Local Adaptive Diffusion Models for Unsupervised Anomaly Detection [60.78684630040313]
  Diffusion models tend to reconstruct normal counterparts of test images with certain noises added. From the global perspective, the difficulty of reconstructing images with different anomalies is uneven. We propose a global and local adaptive diffusion model (abbreviated to GLAD) for unsupervised anomaly detection.
  arXiv  Detail & Related papers  (2024-06-11T17:27:23Z)
• Metric Flow Matching for Smooth Interpolations on the Data Manifold [40.24392451848883]
  Metric Flow Matching (MFM) is a novel simulation-free framework for conditional flow matching. We propose MFM as a framework for conditional paths that transform a source distribution into a target distribution. We test MFM on a suite of challenges including LiDAR navigation, unpaired image translation, and modeling cellular dynamics.
  arXiv  Detail & Related papers  (2024-05-23T16:48:06Z)
• Generating and Reweighting Dense Contrastive Patterns for Unsupervised Anomaly Detection [59.34318192698142]
  We introduce a prior-less anomaly generation paradigm and develop an innovative unsupervised anomaly detection framework named GRAD. PatchDiff effectively expose various types of anomaly patterns. experiments on both MVTec AD and MVTec LOCO datasets also support the aforementioned observation.
  arXiv  Detail & Related papers  (2023-12-26T07:08:06Z)
• MSFlow: Multi-Scale Flow-based Framework for Unsupervised Anomaly Detection [124.52227588930543]
  Unsupervised anomaly detection (UAD) attracts a lot of research interest and drives widespread applications. An inconspicuous yet powerful statistics model, the normalizing flows, is appropriate for anomaly detection and localization in an unsupervised fashion. We propose a novel Multi-Scale Flow-based framework dubbed MSFlow composed of asymmetrical parallel flows followed by a fusion flow. Our MSFlow achieves a new state-of-the-art with a detection AUORC score of up to 99.7%, localization AUCROC score of 98.8%, and PRO score of 97.1%.
  arXiv  Detail & Related papers  (2023-08-29T13:38:35Z)
• Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers [90.45898746733397]
  We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. We show that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current gradient.
  arXiv  Detail & Related papers  (2023-03-06T18:59:19Z)
• Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theories [6.222204646855336]
  We study the consequences of mode-collapse of normalizing flows in the context of lattice field theory. We propose a metric to quantify the degree of mode-collapse and derive a bound on the resulting bias.
  arXiv  Detail & Related papers  (2023-02-27T19:00:22Z)
• ManiFlow: Implicitly Representing Manifolds with Normalizing Flows [145.9820993054072]
  Normalizing Flows (NFs) are flexible explicit generative models that have been shown to accurately model complex real-world data distributions. We propose an optimization objective that recovers the most likely point on the manifold given a sample from the perturbed distribution. Finally, we focus on 3D point clouds for which we utilize the explicit nature of NFs, i.e. surface normals extracted from the gradient of the log-likelihood and the log-likelihood itself.
  arXiv  Detail & Related papers  (2022-08-18T16:07:59Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.