The basis assumption that "training and test data drawn from the same distribution" is often violated in reality. In this paper, we propose one common solution to cover various scenarios of learning under "different but related distributions" in a single framework. Explicit examples include (a) sample selection bias between training and testing data, (b) transfer learning or no labeled data in target domain, and (c) noisy or uncertain training data. The main motivation is that one could ideally solve as many problems as possible with a single approach. The proposed solution extends graph transduction using the maximum margin principle over unlabeled data. The error of the proposed method is bounded under reasonable assumptions even when the training and testing distributions are different. Experiment results demonstrate that the proposed method improves the traditional graph transduction by as much as 15% in accuracy and AUC in all common situations of distribution difference. Most importantly, it outperforms, by up to 10% in accuracy, several state-of-art approaches proposed to solve specific category of distribution difference, i.e, BRSD  for sample selection bias, CDSC  for transfer learning, etc. The main claim is that the adaptive graph transduction is a general and competitive method to solve distribution differences implicitly without knowing and worrying about the exact type. These at least include sample selection bias, transfer learning, uncertainty mining, as well as those alike that are still not studied yet. The source code and datasets are available from the authors.