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We investigate and characterize the inherent resilience of conditional Generative Adversarial Networks (cGANs) against noise in their conditioning labels, and exploit this fact in the context of Unsupervised Domain Adaptation (UDA). In UDA, a classifier trained on the labelled source set can be used to infer pseudo-labels on the unlabelled target set. However, this will result in a significant amount of misclassified examples (due to the well-known domain shift issue), which can be interpreted as noise injection in the ground-truth labels for the target set. We show that cGANs are, to some extent, robust against such "shift noise". Indeed, cGANs trained with noisy pseudo-labels, are able to filter such noise and generate cleaner target samples. We exploit this finding in an iterative procedure where a generative model and a classifier are jointly trained: in turn, the generator allows to sample cleaner data from the target distribution, and the classifier allows to associate better labels to target samples, progressively refining target pseudo-labels. Results on common benchmarks show that our method performs better or comparably with the unsupervised domain adaptation state of the art.