# MathPhys-Guided Coarse-to-Fine Anomaly Synthesis with SQE-Driven Bi-Level Optimization for Anomaly Detection

arXiv: https://arxiv.org/abs/2504.12970 · HTML: https://mlsanity.com/paper/2504.12970/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 17 Apr 2025.

## Builds on (most cited first, 29 of 29)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [CutPaste: Self-Supervised Learning for Anomaly Detection and Localization](https://mlsanity.com/paper/2104.04015/) (2021)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [DRAEM -- A discriminatively trained reconstruction embedding for surface anomaly detection](https://mlsanity.com/paper/2108.07610/) (2021)
- [Anomaly Detection via Reverse Distillation from One-Class Embedding](https://mlsanity.com/paper/2201.10703/) (2022)
- [GANomaly: Semi-Supervised Anomaly Detection via Adversarial Training](https://mlsanity.com/paper/1805.06725/) (2018)
- [SPot-the-Difference Self-Supervised Pre-training for Anomaly Detection and Segmentation](https://mlsanity.com/paper/2207.14315/) (2022)
- [Sub-Image Anomaly Detection with Deep Pyramid Correspondences](https://mlsanity.com/paper/2005.02357/) (2020)
- [VOS: Learning What You Don't Know by Virtual Outlier Synthesis](https://mlsanity.com/paper/2202.01197/) (2022)
- [Multiresolution Knowledge Distillation for Anomaly Detection](https://mlsanity.com/paper/2011.11108/) (2020)
- [SimpleNet: A Simple Network for Image Anomaly Detection and Localization](https://mlsanity.com/paper/2303.15140/) (2023)
- [Diffusion Models for Medical Anomaly Detection](https://mlsanity.com/paper/2203.04306/) (2022)
- [VT-ADL: A Vision Transformer Network for Image Anomaly Detection and Localization](https://mlsanity.com/paper/2104.10036/) (2021)
- [OCGAN: One-class Novelty Detection Using GANs with Constrained Latent Representations](https://mlsanity.com/paper/1903.08550/) (2019)
- [Natural Synthetic Anomalies for Self-Supervised Anomaly Detection and Localization](https://mlsanity.com/paper/2109.15222/) (2021)
- [RealNet: A Feature Selection Network with Realistic Synthetic Anomaly for Anomaly Detection](https://mlsanity.com/paper/2403.05897/) (2024)
- [AnomalyDiffusion: Few-Shot Anomaly Image Generation with Diffusion Model](https://mlsanity.com/paper/2312.05767/) (2023)
- [DSR -- A dual subspace re-projection network for surface anomaly detection](https://mlsanity.com/paper/2208.01521/) (2022)
- [On Diffusion Modeling for Anomaly Detection](https://mlsanity.com/paper/2305.18593/) (2023)
- [Anomaly Detection with Conditioned Denoising Diffusion Models](https://mlsanity.com/paper/2305.15956/) (2023)
- [TransFusion -- A Transparency-Based Diffusion Model for Anomaly Detection](https://mlsanity.com/paper/2311.09999/) (2023)
- [Diversified Outlier Exposure for Out-of-Distribution Detection via Informative Extrapolation](https://mlsanity.com/paper/2310.13923/) (2023)
- [Generative Semi-supervised Graph Anomaly Detection](https://mlsanity.com/paper/2402.11887/) (2024)
- [Text-Guided Variational Image Generation for Industrial Anomaly Detection and Segmentation](https://mlsanity.com/paper/2403.06247/) (2024)
- [A Comprehensive Augmentation Framework for Anomaly Detection](https://mlsanity.com/paper/2308.15068/) (2023)
- [Enhancing Anomaly Detection via Generating Diversified and Hard-to-distinguish Synthetic Anomalies](https://mlsanity.com/paper/2409.10069/) (2024)
- [Friend or Foe? Harnessing Controllable Overfitting for Anomaly Detection](https://mlsanity.com/paper/2412.00560/) (2024)

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

- [Quality-Aware Language-Conditioned Local Auto-Regressive Anomaly Synthesis and Detection](https://mlsanity.com/paper/2508.03539/) (2025)

## Abstract (arXiv)

Currently, industrial anomaly detection suffers from two bottlenecks: (i) the rarity of real-world defect images and (ii) the opacity of sample quality when synthetic data are used. Existing synthetic strategies (e.g., cut-and-paste) overlook the underlying physical causes of defects, leading to inconsistent, low-fidelity anomalies that hamper model generalization to real-world complexities. In this paper, we introduce a novel and lightweight pipeline that generates synthetic anomalies through Math-Phys model guidance, refines them via a Coarse-to-Fine approach and employs a bi-level optimization strategy with a Synthesis Quality Estimator (SQE). By combining physical modeling of the three most typical physics-driven defect mechanisms: Fracture Line (FL), Pitting Loss (PL), and Plastic Warpage (PW), our method produces realistic defect masks, which are subsequently enhanced in two phases. The first stage (npcF) enforces a PDE-based consistency to achieve a globally coherent anomaly structure, while the second stage (npcF++) further improves local fidelity. Additionally, we leverage SQE-driven weighting, ensuring that high-quality synthetic samples receive greater emphasis during training. To validate our method, we conduct experiments on three anomaly detection benchmarks: MVTec AD, VisA, and BTAD. Across these datasets, our method achieves state-of-the-art results in both image- and pixel-AUROC, confirming the effectiveness of our MaPhC2F dataset and BiSQAD method. All code will be released.