Unsupervised Domain Adaptive Semantic Segmentation (UDA-SS) aims to transfer the supervision from a labeled source domain to an unlabeled target domain. The majority of existing UDA-SS works typically consider images whilst recent attempts have extended further to tackle videos by modeling the temporal dimension. Although the two lines of research share the major challenges -- overcoming the underlying domain distribution shift, their studies are largely independent, resulting in fragmented insights, a lack of holistic understanding, and missed opportunities for cross-pollination of ideas. This fragmentation prevents the unification of methods, leading to redundant efforts and suboptimal knowledge transfer across image and video domains. Under this observation, we advocate unifying the study of UDA-SS across video and image scenarios, enabling a more comprehensive understanding, synergistic advancements, and efficient knowledge sharing. To that end, we explore the unified UDA-SS from a general data augmentation perspective, serving as a unifying conceptual framework, enabling improved generalization, and potential for cross-pollination of ideas, ultimately contributing to the overall progress and practical impact of this field of research. Specifically, we propose a Quad-directional Mixup (QuadMix) method, characterized by tackling distinct point attributes and feature inconsistencies through four-directional paths for intra- and inter-domain mixing in a feature space. To deal with temporal shifts with videos, we incorporate optical flow-guided feature aggregation across spatial and temporal dimensions for fine-grained domain alignment. Extensive experiments show that our method outperforms the state-of-the-art works by large margins on four challenging UDA-SS benchmarks. Our source code and models will be released at https://github.com/ZHE-SAPI/UDASS.

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