Integrating Ordinary Differential Equations (ODEs) with U-shaped neural networks has emerged as a novel direction in medical image segmentation. Current networks predominantly employ discretization methods incorporating ODEs. However, these methods face inherent trade-offs between model compactness, computational accuracy, and efficiency. Continuous ODE solutions were rarely studied because they face three limitations: high computational costs, long training time, and poor generalization ability. To address these limitations, we propose an innovative Continuous Neural Memory ODE UNet (CNM-UNet), which replaces all hierarchical decoder layers in vanilla UNet with a single Continuous Neural Memory ODEs Block (CNM-Block) decoder, significantly reducing computation costs and improving training efficiency. CNM-UNet leverages ODEs' dynamic properties to establish continuous temporal feature extraction. For alleviating the generalization problem, a DUal SElf-updated (DUSE) strategy based on test-time adaptation principles is introduced to enhance cross-domain generalization. Experimental results demonstrate CNM-UNet's comprehensive advantages in computational capacity, convergence speed, and cross-domain adaptability, offering new insights for practical deployment of continuous ODE methodologies for medical image segmentation.