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

arXiv: https://arxiv.org/abs/2508.05461 · HTML: https://mlsanity.com/paper/2508.05461/

## Key facts

- Cited by 1 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 57 of its 78 references that are in the map.
- First posted on arXiv 7 Aug 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, 30 of 57)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [DRAEM -- A discriminatively trained reconstruction embedding for surface anomaly detection](https://mlsanity.com/paper/2108.07610/) (2021)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Anomaly Detection via Reverse Distillation from One-Class Embedding](https://mlsanity.com/paper/2201.10703/) (2022)
- [SPot-the-Difference Self-Supervised Pre-training for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2207.14315/) (2022)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Sub-Image Anomaly Detection with Deep Pyramid Correspondences](https://mlsanity.com/paper/2005.02357/) (2020)
- [A Unified Model for Multi-class Anomaly Detection](https://mlsanity.com/paper/2206.03687/) (2022)
- [SimpleNet: A Simple Network for Image Anomaly Detection and Localization](https://mlsanity.com/paper/2303.15140/) (2023)
- [FastFlow: Unsupervised Anomaly Detection and Localization via 2D Normalizing Flows](https://mlsanity.com/paper/2111.07677/) (2021)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Same Same But DifferNet: Semi-Supervised Defect Detection with Normalizing Flows](https://mlsanity.com/paper/2008.12577/) (2020)
- [The MVTec 3D-AD Dataset for Unsupervised 3D Anomaly Detection and Localization](https://mlsanity.com/paper/2112.09045/) (2021)
- [EfficientAD: Accurate Visual Anomaly Detection at Millisecond-Level Latencies](https://mlsanity.com/paper/2303.14535/) (2023)

## Built on by (most cited first, 1 of 1)

- [Mitigating Convergence Collapse in Fixed-Target Anomaly Detectors via Kernel-Anchored Locality Regularization](https://mlsanity.com/paper/2610.02345/) (2026)

## Abstract (arXiv)

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.