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Generalizing models trained on normal visual conditions to target domains under adverse conditions is demanding in the practical systems. One prevalent solution is to bridge the domain gap between clear- and adverse-condition images to make satisfactory prediction on the target. However, previous methods often reckon on additional reference images of the same scenes taken from normal conditions, which are quite tough to collect in reality. Furthermore, most of them mainly focus on individual adverse condition such as nighttime or foggy, weakening the model versatility when encountering other adverse weathers. To overcome the above limitations, we propose a novel framework, Visibility Boosting and Logit-Constraint learning (VBLC), tailored for superior normal-to-adverse adaptation. VBLC explores the potential of getting rid of reference images and resolving the mixture of adverse conditions simultaneously. In detail, we first propose the visibility boost module to dynamically improve target images via certain priors in the image level. Then, we figure out the overconfident drawback in the conventional cross-entropy loss for self-training method and devise the logit-constraint learning, which enforces a constraint on logit outputs during training to mitigate this pain point. To the best of our knowledge, this is a new perspective for tackling such a challenging task. Extensive experiments on two normal-to-adverse domain adaptation benchmarks, i.e., Cityscapes -> ACDC and Cityscapes -> FoggyCityscapes + RainCityscapes, verify the effectiveness of VBLC, where it establishes the new state of the art. Code is available at https://github.com/BIT-DA/VBLC.