# Fully Convolutional Cross-Scale-Flows for Image-based Defect Detection

arXiv: https://arxiv.org/abs/2110.02855 · HTML: https://mlsanity.com/paper/2110.02855/

## Key facts

- Cited by 117 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (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)
- [Deep High-Resolution Representation Learning for Human Pose Estimation](https://mlsanity.com/paper/1902.09212/) (2019)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [GANomaly: Semi-Supervised Anomaly Detection via Adversarial Training](https://mlsanity.com/paper/1805.06725/) (2018)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders](https://mlsanity.com/paper/1807.02011/) (2018)
- [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)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Explainable Deep One-Class Classification](https://mlsanity.com/paper/2007.01760/) (2020)
- [Modeling the Distribution of Normal Data in Pre-Trained Deep Features for Anomaly Detection](https://mlsanity.com/paper/2005.14140/) (2020)
- [Deep Structured Energy Based Models for Anomaly Detection](https://mlsanity.com/paper/1605.07717/) (2016)
- [Probabilistic Monocular 3D Human Pose Estimation with Normalizing Flows](https://mlsanity.com/paper/2107.13788/) (2021)
- [TOAD-GAN: Coherent Style Level Generation from a Single Example](https://mlsanity.com/paper/2008.01531/) (2020)
- [Are pre-trained CNNs good feature extractors for anomaly detection in surveillance videos?](https://mlsanity.com/paper/1811.08495/) (2018)
- [Structuring Autoencoders](https://mlsanity.com/paper/1908.02626/) (2019)
- [Anomaly Detection in Trajectory Data with Normalizing Flows](https://mlsanity.com/paper/2004.05958/) (2020)
- [Normalizing flows for novelty detection in industrial time series data](https://mlsanity.com/paper/1906.06904/) (2019)
- [Video Event Recognition and Anomaly Detection by Combining Gaussian Process and Hierarchical Dirichlet Process Models](https://mlsanity.com/paper/1802.03257/) (2018)

## Built on by (most cited first, 30 of 117)

- [SPot-the-Difference Self-Supervised Pre-training for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2207.14315/) (2022)
- [SimpleNet: A Simple Network for Image Anomaly Detection and Localization](https://mlsanity.com/paper/2303.15140/) (2023)
- [EfficientAD: Accurate Visual Anomaly Detection at Millisecond-Level Latencies](https://mlsanity.com/paper/2303.14535/) (2023)
- [Deep Industrial Image Anomaly Detection: A Survey](https://mlsanity.com/paper/2301.11514/) (2023)
- [Real-IAD: A Real-World Multi-View Dataset for Benchmarking Versatile Industrial Anomaly Detection](https://mlsanity.com/paper/2403.12580/) (2024)
- [Asymmetric Student-Teacher Networks for Industrial Anomaly Detection](https://mlsanity.com/paper/2210.07829/) (2022)
- [BMAD: Benchmarks for Medical Anomaly Detection](https://mlsanity.com/paper/2306.11876/) (2023)
- [PyramidFlow: High-Resolution Defect Contrastive Localization using Pyramid Normalizing Flow](https://mlsanity.com/paper/2303.02595/) (2023)
- [Deep Learning for Unsupervised Anomaly Localization in Industrial Images: A Survey](https://mlsanity.com/paper/2207.10298/) (2022)
- [IM-IAD: Industrial Image Anomaly Detection Benchmark in Manufacturing](https://mlsanity.com/paper/2301.13359/) (2023)
- [Prototypical Residual Networks for Anomaly Detection and Localization](https://mlsanity.com/paper/2212.02031/) (2022)
- [AnomalyDINO: Boosting Patch-based Few-shot Anomaly Detection with DINOv2](https://mlsanity.com/paper/2405.14529/) (2024)
- [DiffusionAD: Norm-guided One-step Denoising Diffusion for Anomaly Detection](https://mlsanity.com/paper/2303.08730/) (2023)
- [PAD: A Dataset and Benchmark for Pose-agnostic Anomaly Detection](https://mlsanity.com/paper/2310.07716/) (2023)
- [TransFusion -- A Transparency-Based Diffusion Model for Anomaly Detection](https://mlsanity.com/paper/2311.09999/) (2023)
- [Cheating Depth: Enhancing 3D Surface Anomaly Detection via Depth Simulation](https://mlsanity.com/paper/2311.01117/) (2023)
- [Focus the Discrepancy: Intra- and Inter-Correlation Learning for Image Anomaly Detection](https://mlsanity.com/paper/2308.02983/) (2023)
- [Unsupervised Continual Anomaly Detection with Contrastively-learned Prompt](https://mlsanity.com/paper/2401.01010/) (2024)
- [The MVTec AD 2 Dataset: Advanced Scenarios for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2503.21622/) (2025)
- [AdaptCLIP: Adapting CLIP for Universal Visual Anomaly Detection](https://mlsanity.com/paper/2505.09926/) (2025)
- [Hierarchical Gaussian Mixture Normalizing Flow Modeling for Unified Anomaly Detection](https://mlsanity.com/paper/2403.13349/) (2024)
- [MSFlow: Multi-Scale Flow-based Framework for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2308.15300/) (2023)
- [SplatPose & Detect: Pose-Agnostic 3D Anomaly Detection](https://mlsanity.com/paper/2404.06832/) (2024)
- [ResAD: A Simple Framework for Class Generalizable Anomaly Detection](https://mlsanity.com/paper/2410.20047/) (2024)
- [Component-aware anomaly detection framework for adjustable and logical industrial visual inspection](https://mlsanity.com/paper/2305.08509/) (2023)
- [A Survey on Unsupervised Anomaly Detection Algorithms for Industrial Images](https://mlsanity.com/paper/2204.11161/) (2022)
- [Learning Unified Reference Representation for Unsupervised Multi-class Anomaly Detection](https://mlsanity.com/paper/2403.11561/) (2024)
- [Reconstruction from edge image combined with color and gradient difference for industrial surface anomaly detection](https://mlsanity.com/paper/2210.14485/) (2022)
- [Learning to Detect Multi-class Anomalies with Just One Normal Image Prompt](https://mlsanity.com/paper/2505.09264/) (2025)
- [Progressive Boundary Guided Anomaly Synthesis for Industrial Anomaly Detection](https://mlsanity.com/paper/2412.17458/) (2024)

## Abstract (arXiv)

In industrial manufacturing processes, errors frequently occur at unpredictable times and in unknown manifestations. We tackle the problem of automatic defect detection without requiring any image samples of defective parts. Recent works model the distribution of defect-free image data, using either strong statistical priors or overly simplified data representations. In contrast, our approach handles fine-grained representations incorporating the global and local image context while flexibly estimating the density. To this end, we propose a novel fully convolutional cross-scale normalizing flow (CS-Flow) that jointly processes multiple feature maps of different scales. Using normalizing flows to assign meaningful likelihoods to input samples allows for efficient defect detection on image-level. Moreover, due to the preserved spatial arrangement the latent space of the normalizing flow is interpretable which enables to localize defective regions in the image. Our work sets a new state-of-the-art in image-level defect detection on the benchmark datasets Magnetic Tile Defects and MVTec AD showing a 100% AUROC on 4 out of 15 classes.