Anomaly detection is critical in industrial manufacturing for ensuring product quality and improving efficiency in automated processes. The scarcity of anomalous samples limits traditional detection methods, making anomaly generation essential for expanding the data repository. However, recent generative models often produce unrealistic anomalies increasing false positives, or require real-world anomaly samples for training. In this work, we treat anomaly generation as a compositional problem and propose ComGEN, a component-aware and unsupervised framework that addresses the gap in logical anomaly generation. Our method comprises a multi-component learning strategy to disentangle visual components, followed by subsequent generation editing procedures. Disentangled text-to-component pairs, revealing intrinsic logical constraints, conduct attention-guided residual mapping and model training with iteratively matched references across multiple scales. Experiments on the MVTecLOCO dataset confirm the efficacy of ComGEN, achieving the best AUROC score of 91.2%. Additional experiments on the real-world scenario of Diesel Engine and widely-used MVTecAD dataset demonstrate significant performance improvements when integrating simulated anomalies generated by ComGEN into automated production workflows.