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Accurate infarct segmentation in non-contrast CT (NCCT) images is a crucial step toward computer-aided acute ischemic stroke (AIS) assessment. In clinical practice, bilateral symmetric comparison of brain hemispheres is usually used to locate pathological abnormalities. Recent research has explored asymmetries to assist with AIS segmentation. However, most previous symmetry-based work mixed different types of asymmetries when evaluating their contribution to AIS. In this paper, we propose a novel Asymmetry Disentanglement Network (ADN) to automatically separate pathological asymmetries and intrinsic anatomical asymmetries in NCCTs for more effective and interpretable AIS segmentation. ADN first performs asymmetry disentanglement based on input NCCTs, which produces different types of 3D asymmetry maps. Then a synthetic, intrinsic-asymmetry-compensated and pathology-asymmetry-salient NCCT volume is generated and later used as input to a segmentation network. The training of ADN incorporates domain knowledge and adopts a tissue-type aware regularization loss function to encourage clinically-meaningful pathological asymmetry extraction. Coupled with an unsupervised 3D transformation network, ADN achieves state-of-the-art AIS segmentation performance on a public NCCT dataset. In addition to the superior performance, we believe the learned clinically-interpretable asymmetry maps can also provide insights towards a better understanding of AIS assessment. Our code is available at https://github.com/nihaomiao/MICCAI22_ADN.