# U-Flow: A U-shaped Normalizing Flow for Anomaly Detection with Unsupervised Threshold

arXiv: https://arxiv.org/abs/2211.12353 · HTML: https://mlsanity.com/paper/2211.12353/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 70 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Multiscale Vision Transformers](https://mlsanity.com/paper/2104.11227/) (2021)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [Going deeper with Image Transformers](https://mlsanity.com/paper/2103.17239/) (2021)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [CutPaste: Self-Supervised Learning for Anomaly Detection and Localization](https://mlsanity.com/paper/2104.04015/) (2021)
- [GANomaly: Semi-Supervised Anomaly Detection via Adversarial Training](https://mlsanity.com/paper/1805.06725/) (2018)
- [Future Frame Prediction for Anomaly Detection -- A New Baseline](https://mlsanity.com/paper/1712.09867/) (2017)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [Sub-Image Anomaly Detection with Deep Pyramid Correspondences](https://mlsanity.com/paper/2005.02357/) (2020)
- [Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders](https://mlsanity.com/paper/1807.02011/) (2018)
- [FastFlow: Unsupervised Anomaly Detection and Localization via 2D Normalizing Flows](https://mlsanity.com/paper/2111.07677/) (2021)
- [VT-ADL: A Vision Transformer Network for Image Anomaly Detection and Localization](https://mlsanity.com/paper/2104.10036/) (2021)
- [Patch SVDD: Patch-level SVDD for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2006.16067/) (2020)
- [Same Same But DifferNet: Semi-Supervised Defect Detection with Normalizing Flows](https://mlsanity.com/paper/2008.12577/) (2020)
- [i-RevNet: Deep Invertible Networks](https://mlsanity.com/paper/1802.07088/) (2018)
- [CFA: Coupled-hypersphere-based Feature Adaptation for Target-Oriented Anomaly Localization](https://mlsanity.com/paper/2206.04325/) (2022)
- [Fully Convolutional Cross-Scale-Flows for Image-based Defect Detection](https://mlsanity.com/paper/2110.02855/) (2021)

## Built on by (most cited first, 16 of 16)

- [R3D-AD: Reconstruction via Diffusion for 3D Anomaly Detection](https://mlsanity.com/paper/2407.10862/) (2024)
- [TransFusion -- A Transparency-Based Diffusion Model for Anomaly Detection](https://mlsanity.com/paper/2311.09999/) (2023)
- [Target before Shooting: Accurate Anomaly Detection and Localization under One Millisecond via Cascade Patch Retrieval](https://mlsanity.com/paper/2308.06748/) (2023)
- [Anomaly Detection and Generation with Diffusion Models: A Survey](https://mlsanity.com/paper/2506.09368/) (2025)
- [Foundation Models and Transformers for Anomaly Detection: A Survey](https://mlsanity.com/paper/2507.15905/) (2025)
- [Industrial Anomaly Detection and Localization Using Weakly-Supervised Residual Transformers](https://mlsanity.com/paper/2306.03492/) (2023)
- [RAD: A Dataset and Benchmark for Real-Life Anomaly Detection with Robotic Observations](https://mlsanity.com/paper/2410.00713/) (2024)
- [AUPIMO: Redefining Visual Anomaly Detection Benchmarks with High Speed and Low Tolerance](https://mlsanity.com/paper/2401.01984/) (2024)
- [Dissolving Is Amplifying: Towards Fine-Grained Anomaly Detection](https://mlsanity.com/paper/2302.14696/) (2023)
- [FlowCLAS: Enhancing Normalizing Flow Via Contrastive Learning For Anomaly Segmentation](https://mlsanity.com/paper/2411.19888/) (2024)
- [ISP-AD: A Large-Scale Real-World Dataset for Advancing Industrial Anomaly Detection with Synthetic and Real Defects](https://mlsanity.com/paper/2503.04997/) (2025)
- [CL-Flow:Strengthening the Normalizing Flows by Contrastive Learning for Better Anomaly Detection](https://mlsanity.com/paper/2311.06794/) (2023)
- [On Uniformly Scaling Flows: A Density-Aligned Approach to Deep One-Class Classification](https://mlsanity.com/paper/2510.09452/) (2025)
- [Two Steps Are All You Need: Efficient 3D Point Cloud Anomaly Detection with Consistency Models](https://mlsanity.com/paper/2605.05372/) (2026)
- [Visual Prompting Meets Feature Reconstruction-Based Anomaly Detection with Dual-Teacher Supervision](https://mlsanity.com/paper/2606.09670/) (2026)
- [From Benchmark Performance to Tool Deployment: Human-in-the-Loop Anomaly Detection](https://mlsanity.com/paper/2608.07770/) (2026)

## Abstract (arXiv)

In this work we propose a one-class self-supervised method for anomaly segmentation in images that benefits both from a modern machine learning approach and a more classic statistical detection theory. The method consists of four phases. First, features are extracted using a multi-scale image Transformer architecture. Then, these features are fed into a U-shaped Normalizing Flow (NF) that lays the theoretical foundations for the subsequent phases. The third phase computes a pixel-level anomaly map from the NF embedding, and the last phase performs a segmentation based on the a contrario framework. This multiple hypothesis testing strategy permits the derivation of robust unsupervised detection thresholds, which are crucial in real-world applications where an operational point is needed. The segmentation results are evaluated using the Mean Intersection over Union (mIoU) metric, and for assessing the generated anomaly maps we report the area under the Receiver Operating Characteristic curve (AUROC), as well as the Area Under the Per-Region-Overlap curve (AUPRO). Extensive experimentation in various datasets shows that the proposed approach produces state-of-the-art results for all metrics and all datasets, ranking first in most MVTec-AD categories, with a mean pixel-level AUROC of 98.74%. Code and trained models are available at https:// github.com/mtailanian/uflow.