# Scalable, Explainable and Provably Robust Anomaly Detection with One-Step Flow Matching

arXiv: https://arxiv.org/abs/2510.18328 · HTML: https://mlsanity.com/paper/2510.18328/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 14 of its 108 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 14 of 14)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [Flow Matching in Latent Space](https://mlsanity.com/paper/2307.08698/) (2023)
- [On Diffusion Modeling for Anomaly Detection](https://mlsanity.com/paper/2305.18593/) (2023)
- [Generative Adversarial Networks](https://mlsanity.com/paper/1406.2661/) (2014)
- [Unsupervised anomaly localization using VAE and beta-VAE](https://mlsanity.com/paper/2005.10686/) (2020)
- [Diffusion and Flow Matching Models for Tabular Data: A Survey](https://mlsanity.com/paper/2502.17119/) (2025)

## Built on by (most cited first, 9 of 9)

- [TACTIC for Navigating the Unknown: Tabular Anomaly deteCTion via In-Context inference](https://mlsanity.com/paper/2603.14171/) (2026)
- [Flow Mismatching: Unsupervised Anomaly Detection via Velocity Discrepancies in Flow Matching Models](https://mlsanity.com/paper/2605.23070/) (2026)
- [Scalable anomaly detection via a univariate Christoffel function](https://mlsanity.com/paper/2606.12483/) (2026)
- [Automatic Unsupervised Ensemble Outlier Model Selection--Extended Version](https://mlsanity.com/paper/2605.16567/) (2026)
- [ReFP-AD: Rectified Flow Preconditioning for Energy-Based Anomaly Detection](https://mlsanity.com/paper/2608.01793/) (2026)
- [MVFM-3DAD: Multi-view Flow Matching for 3D Anomaly Detection via Density Proxy Estimation](https://mlsanity.com/paper/2608.12148/) (2026)
- [Unsupervised Anomaly Detection Using Flow Matching on Tabular Data](https://mlsanity.com/paper/2608.19801/) (2026)
- [Differentiable Interval Bottlenecks for Interpretable Anomaly Detection in Numerical Data](https://mlsanity.com/paper/2609.03878/) (2026)
- [Mitigating Convergence Collapse in Fixed-Target Anomaly Detectors via Kernel-Anchored Locality Regularization](https://mlsanity.com/paper/2610.02345/) (2026)

## Abstract (arXiv)

We introduce Time-Conditioned Contraction Matching (TCCM), a novel method for semi-supervised anomaly detection in tabular data. TCCM is inspired by flow matching, a recent generative modeling framework that learns velocity fields between probability distributions and has shown strong performance compared to diffusion models and generative adversarial networks. Instead of directly applying flow matching as originally formulated, TCCM builds on its core idea -- learning velocity fields between distributions -- but simplifies the framework by predicting a time-conditioned contraction vector toward a fixed target (the origin) at each sampled time step. This design offers three key advantages: (1) a lightweight and scalable training objective that removes the need for solving ordinary differential equations during training and inference; (2) an efficient scoring strategy called one time-step deviation, which quantifies deviation from expected contraction behavior in a single forward pass, addressing the inference bottleneck of existing continuous-time models such as DTE (a diffusion-based model with leading anomaly detection accuracy but heavy inference cost); and (3) explainability and provable robustness, as the learned velocity field operates directly in input space, making the anomaly score inherently feature-wise attributable; moreover, the score function is Lipschitz-continuous with respect to the input, providing theoretical guarantees under small perturbations. Extensive experiments on the ADBench benchmark show that TCCM strikes a favorable balance between detection accuracy and inference cost, outperforming state-of-the-art methods -- especially on high-dimensional and large-scale datasets. The source code is available at our GitHub repository.