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- Abstract: In unsupervised domain adaptation (UDA), classifiers for the target domain (TD) are trained with clean labeled data from the source domain (SD) and unlabeled data from TD. However, in the wild, it is hard to acquire a large amount of perfectly clean labeled data in SD given limited budget. Hence, we consider a new, more realistic and more challenging problem setting, where classifiers have to be trained with noisy labeled data from SD and unlabeled data from TD---we name it wildly UDA (WUDA). We show that WUDA ruins all UDA methods if taking no care of label noise in SD, and to this end, we propose a Butterfly framework, a powerful and efficient solution to WUDA. Butterfly maintains four models (e.g., deep networks) simultaneously, where two take care of all adaptations (i.e., noisy-to-clean, labeled-to-unlabeled, and SD-to-TD-distributional) and then the other two can focus on classification in TD. As a consequence, Butterfly possesses all the conceptually necessary components for solving WUDA. Experiments demonstrate that under WUDA, Butterfly significantly outperforms existing baseline methods.