Deep learning (DL) models for segmenting various anatomical structures have achieved great success via a static DL model that is trained in a single source domain. Yet, the static DL model is likely to perform poorly in a continually evolving environment, requiring appropriate model updates. In an incremental learning setting, we would expect that well-trained static models are updated, following continually evolving target domain data—e.g., additional lesions or structures of interest—collected from different sites, without catastrophic forgetting. This, however, poses challenges, due to distribution shifts, additional structures not seen during the initial model training, and the absence of training data in a source domain. To address these challenges, in this work, we seek to progressively evolve an “off-the-shelf” trained segmentation model to diverse datasets with additional anatomical categories in a unified manner. Specifically, we first propose a divergence-aware dual-flow module with balanced rigidity and plasticity branches to decouple old and new tasks, which is guided by continuous batch renormalization. Then, a complementary pseudo-label training scheme with self-entropy regularized momentum MixUp decay is developed for adaptive network optimization. We evaluated our framework on a brain tumor segmentation task with continually changing target domains—i.e., new MRI scanners/modalities with incremental structures. Our framework was able to well retain the discriminability of previously learned structures, hence enabling the realistic life-long segmentation model extension along with the widespread accumulation of big medical data.