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

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.