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Previous unsupervised domain adaptation (UDA) methods aim to promote target learning via a single-directional knowledge transfer from label-rich source domain to unlabeled target domain, while its reverse adaption from target to source has not jointly been considered yet so far. In fact, in some real teaching practice, a teacher helps students learn while also gets promotion from students to some extent, which inspires us to explore a dual-directional knowledge transfer between domains, and thus propose a Dual-Correction Adaptation Network (DualCAN) in this paper. However, due to the asymmetrical label knowledge across domains, transfer from unlabeled target to labeled source poses a more difficult challenge than the common source-to-target counterpart. First, the target pseudo-labels predicted by source commonly involve noises due to model bias, hence in the reverse adaptation, they may hurt the source performance and bring a negative target-to-source transfer. Secondly, source domain usually contains innate noises, which will inevitably aggravate the target noises, leading to noise amplification across domains. To this end, we further introduce a Noise Identification and Correction (NIC) module to correct and recycle noises in both domains. To our best knowledge, this is the first naive attempt of dual-directional adaptation for noisy UDA, and naturally applicable to noise-free UDA. A theory justification is given to state the rationality of our intuition. Empirical results confirm the effectiveness of DualCAN with remarkable performance gains over state-of-the-arts, particularly for extreme noisy tasks (e.g., ~+ 15% on Pw->Pr and Pr->Rw of Office-Home).