Bad training data would challenge the learning model from understanding the underlying data-generating scheme, which then increases the difficulty in achieving satisfactory performance on unseen test data. We suppose the real data distribution lies in a distribution set supported by the empirical distribution of bad data. A worst-case formulation can be developed over this distribution set, and then be interpreted as a generation task in an adversarial manner. The connections and differences between GANs and our framework have been thoroughly discussed. We further theoretically show the influence of this generation task on learning from bad data and reveal its connection with a data-dependent regularization. Given different distance measures (\eg, Wasserstein distance or JS divergence) of distributions, we can derive different objective functions for the problem. Experimental results on different kinds of bad training data demonstrate the necessity and effectiveness of the proposed method.