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 further introduce a new regularization by gathering explicit depth distribution prior to constrain the model facing real-world data.Experiments show that our method outperforms the state-of-the-art across diverse conditions in multi-frame and single-frame settings. We achieve improvements of 7.5\% in AbsRel and 4.3\% in RMSE on average for nuScenes and Robotcar datasets (daytime, nighttime, rain). In zero-shot evaluation on DrivingStereo (rain, fog), our method generalizes better than previous ones. Our code will be released soon.