# Flow Mismatching: Unsupervised Anomaly Detection via Velocity Discrepancies in Flow Matching Models

arXiv: https://arxiv.org/abs/2605.23070 · HTML: https://mlsanity.com/paper/2605.23070/

## Key facts

- Cited by 2 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 22 of its 31 references that are in the map.
- First posted on arXiv 21 May 2026.

## 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, 22 of 22)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [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)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [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)
- [DeSTSeg: Segmentation Guided Denoising Student-Teacher for Anomaly Detection](https://mlsanity.com/paper/2211.11317/) (2022)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [Dinomaly: The Less Is More Philosophy in Multi-Class Unsupervised Anomaly Detection](https://mlsanity.com/paper/2405.14325/) (2024)
- [Hierarchical Vector Quantized Transformer for Multi-class Unsupervised Anomaly Detection](https://mlsanity.com/paper/2310.14228/) (2023)
- [Exploring Plain ViT Reconstruction for Multi-class Unsupervised Anomaly Detection](https://mlsanity.com/paper/2312.07495/) (2023)
- [DiffusionAD: Norm-guided One-step Denoising Diffusion for Anomaly Detection](https://mlsanity.com/paper/2303.08730/) (2023)
- [TransFusion -- A Transparency-Based Diffusion Model for Anomaly Detection](https://mlsanity.com/paper/2311.09999/) (2023)
- [DDPM-MoCo: Advancing Industrial Surface Defect Generation and Detection with Generative and Contrastive Learning](https://mlsanity.com/paper/2407.03332/) (2024)
- [Scalable, Explainable and Provably Robust Anomaly Detection with One-Step Flow Matching](https://mlsanity.com/paper/2510.18328/) (2025)
- [Anomaly Detection for Industrial Applications, Its Challenges, Solutions, and Future Directions: A Review](https://mlsanity.com/paper/2501.11310/) (2025)
- [REFLECT: Rectified Flows for Efficient Brain Anomaly Correction Transport](https://mlsanity.com/paper/2508.02889/) (2025)
- [HDM: Hybrid Diffusion Model for Unified Image Anomaly Detection](https://mlsanity.com/paper/2502.19200/) (2025)
- [Energy-Tweedie: Score meets Score, Energy meets Energy](https://mlsanity.com/paper/2512.23818/) (2025)

## Built on by (most cited first, 2 of 2)

- [MVFM-3DAD: Multi-view Flow Matching for 3D Anomaly Detection via Density Proxy Estimation](https://mlsanity.com/paper/2608.12148/) (2026)
- [Graph-Spectral Flow Matching for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2609.36765/) (2026)

## Abstract (arXiv)

We propose Flow Mismatching, an unsupervised anomaly detection method that deliberately avoids reconstruction-based paradigms. Instead, we treat flow matching as geometric dynamics and leverage a key insight: anomalies occur at places where the learned normal flow disagrees with the geometric path toward a test image. Given a flow matching model trained only on normal images, we probe its learned velocity field along affine paths from Gaussian noise to a target image. Along each path, we compare the model-predicted velocity, which follows normal generative dynamics, with the geometric velocity toward the target, which includes any anomalous content. Anomalies induce strong local disagreement between these velocities. Aggregating the mismatch over different time steps and multiple paths yields pixel-wise heatmaps and image-level scores without test-time optimization, feature memories, or additional calibration. Our analysis shows that the population mismatch decomposes into an irreducible denoising term and a Fisher-divergence term between the test-path and normal-path score functions, which identifies the score-gap component that drives anomaly separation and explains the effectiveness of robust path aggregation. Extensive experiments on MVTec-AD and VisA demonstrate superior performance compared with SOTA reconstruction-based and recent flow matching-based approaches.