Self-supervised depth estimation from monocular cameras in diverse outdoor conditions, such as daytime, rain, and nighttime, is challenging due to the difficulty of learning universal representations and the severe lack of labeled real-world adverse data. Previous methods either rely on synthetic inputs and pseudo-depth labels or directly apply daytime strategies to adverse conditions, resulting in suboptimal results. In this paper, we present the first synthetic-to-real robust depth estimation framework, incorporating motion and structure priors to capture real-world knowledge effectively. In the synthetic adaptation, we transfer motion-structure knowledge inside cost volumes for better robust representation, using a frozen daytime model to train a depth estimator in synthetic adverse conditions. In the innovative real adaptation, which targets to fix synthetic-real gaps, models trained earlier identify the weather-insensitive regions with a designed consistency-reweighting strategy to emphasize valid pseudo-labels. We introduce a new regularization by gathering explicit depth distributions to constrain the model when facing real-world data. Experiments show that our method outperforms the state-of-the-art across diverse conditions in multi-frame and single-frame evaluations. We achieve improvements of 7.5% and 4.3% in AbsRel and RMSE on average for nuScenes and Robotcar datasets (daytime, nighttime, rain). In zero-shot evaluation of DrivingStereo (rain, fog), our method generalizes better than the previous ones.