# Mixture Prototype Flow Matching for Open-Set Supervised Anomaly Detection

arXiv: https://arxiv.org/abs/2605.02438 · HTML: https://mlsanity.com/paper/2605.02438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 28 of its 40 references that are in the map.
- First posted on arXiv 4 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, 28 of 28)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [CutPaste: Self-Supervised Learning for Anomaly Detection and Localization](https://mlsanity.com/paper/2104.04015/) (2021)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Multiresolution Knowledge Distillation for Anomaly Detection](https://mlsanity.com/paper/2011.11108/) (2020)
- [Taming Rectified Flow for Inversion and Editing](https://mlsanity.com/paper/2411.04746/) (2024)
- [Segmentation-Based Deep-Learning Approach for Surface-Defect Detection](https://mlsanity.com/paper/1903.08536/) (2019)
- [AnomalyDiffusion: Few-Shot Anomaly Image Generation with Diffusion Model](https://mlsanity.com/paper/2312.05767/) (2023)
- [Catching Both Gray and Black Swans: Open-set Supervised Anomaly Detection](https://mlsanity.com/paper/2203.14506/) (2022)
- [Graph Embedded Pose Clustering for Anomaly Detection](https://mlsanity.com/paper/1912.11850/) (2019)
- [Dinomaly: The Less Is More Philosophy in Multi-Class Unsupervised Anomaly Detection](https://mlsanity.com/paper/2405.14325/) (2024)
- [Explainable Deep Few-shot Anomaly Detection with Deviation Networks](https://mlsanity.com/paper/2108.00462/) (2021)
- [FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing](https://mlsanity.com/paper/2412.07517/) (2024)
- [Hierarchical Vector Quantized Transformer for Multi-class Unsupervised Anomaly Detection](https://mlsanity.com/paper/2310.14228/) (2023)
- [Automatic Classification of Defective Photovoltaic Module Cells in Electroluminescence Images](https://mlsanity.com/paper/1807.02894/) (2018)
- [Dual-Interrelated Diffusion Model for Few-Shot Anomaly Image Generation](https://mlsanity.com/paper/2408.13509/) (2024)
- [Unsupervised Continual Anomaly Detection with Contrastively-learned Prompt](https://mlsanity.com/paper/2401.01010/) (2024)
- [Hierarchical Gaussian Mixture Normalizing Flow Modeling for Unified Anomaly Detection](https://mlsanity.com/paper/2403.13349/) (2024)
- [Anomaly Heterogeneity Learning for Open-set Supervised Anomaly Detection](https://mlsanity.com/paper/2310.12790/) (2023)
- [Unseen Visual Anomaly Generation](https://mlsanity.com/paper/2406.01078/) (2024)
- [Supervised Anomaly Detection for Complex Industrial Images](https://mlsanity.com/paper/2405.04953/) (2024)
- [Gaussian Mixture Flow Matching Models](https://mlsanity.com/paper/2504.05304/) (2025)
- [Generating and Reweighting Dense Contrastive Patterns for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2312.15911/) (2023)
- [Distribution Prototype Diffusion Learning for Open-set Supervised Anomaly Detection](https://mlsanity.com/paper/2502.20981/) (2025)

## Abstract (arXiv)

Open-set supervised anomaly detection (OSAD) aims to identify unseen anomalies using limited anomalous supervision. However, existing prototype-based methods typically model normal data via a unimodal Gaussian prior, failing to capture inherent multi-modality and resulting in blurred decision boundaries. To address this, we propose Mixture Prototype Flow Matching (MPFM), a framework that learns a continuous transformation from normal feature distributions to a structured Gaussian mixture prototype space. Departing from traditional flow-based approaches that rely on a single velocity vector, MPFM explicitly models the velocity field as a Gaussian mixture prior where each component corresponds to a distinct normal class. This design facilitates mode-aware and semantically coherent distribution transport. Furthermore, we introduce a Mutual Information Maximization Regularizer (MIMR) to prevent prototype collapse and maximize normal-anomaly separability. Extensive experiments demonstrate that MPFM achieves state-of-the-art performance across diverse benchmarks under both single- and multi-anomaly settings.