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Semantic segmentation suffers from significant performance degradation when the trained network is applied to a different domain. To address this issue, unsupervised domain adaptation (UDA) has been extensively studied. Despite the effectiveness of selftraining techniques in UDA, they still overlook the explicit modeling of domain-shared feature extraction. In this paper, we propose DiDA, an unsupervised domain bridging approach for semantic segmentation. DiDA consists of two key modules: (1) Degradation-based Intermediate Domain Construction, which creates continuous intermediate domains through simple image degradation operations to encourage learning domain-invariant features as domain differences gradually diminish; (2) Semantic Shift Compensation, which leverages a diffusion encoder to disentangle and compensate for semantic shift information with degraded time-steps, preserving discriminative representations in the intermediate domains. As a plug-and-play solution, DiDA supports various degradation operations and seamlessly integrates with existing UDA methods. Extensive experiments on multiple domain adaptive semantic segmentation benchmarks demonstrate that DiDA consistently achieves significant performance improvements across all settings. Code is available at https://github.com/Woof6/DiDA.