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Knowledge Distillation-based Anomaly Detection (KDAD) methods rely on the teacher-student paradigm to detect and segment anomalous regions by contrasting the unique features extracted by both networks. However, existing KDAD methods suffer from two main limitations: 1) the student network can effortlessly replicate the teacher network's representations, and 2) the features of the teacher network serve solely as a ``reference standard" and are not fully leveraged. Toward this end, we depart from the established paradigm and instead propose an innovative approach called Asymmetric Distillation Post-Segmentation (ADPS). Our ADPS employs an asymmetric distillation paradigm that takes distinct forms of the same image as the input of the teacher-student networks, driving the student network to learn discriminating representations for anomalous regions. Meanwhile, a customized Weight Mask Block (WMB) is proposed to generate a coarse anomaly localization mask that transfers the distilled knowledge acquired from the asymmetric paradigm to the teacher network. Equipped with WMB, the proposed Post-Segmentation Module (PSM) is able to effectively detect and segment abnormal regions with fine structures and clear boundaries. Experimental results demonstrate that the proposed ADPS outperforms the state-of-the-art methods in detecting and segmenting anomalies. Surprisingly, ADPS significantly improves Average Precision (AP) metric by 9% and 20% on the MVTec AD and KolektorSDD2 datasets, respectively.