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Adversarial learning has achieved remarkable performances for unsupervised domain adaptation (UDA). Existing adversarial UDA methods typically adopt an additional discriminator to play the min-max game with a feature extractor. However, most of these methods failed to effectively leverage the predicted discriminative information, and thus cause mode collapse for generator. In this work, we address this problem from a different perspective and design a simple yet effective adversarial paradigm in the form of a discriminator-free adversarial learning network (DALN), wherein the category classifier is reused as a discriminator, which achieves explicit domain alignment and category distinguishment through a unified objective, enabling the DALN to leverage the predicted discriminative information for sufficient feature alignment. Basically, we introduce a Nuclear-norm Wasserstein discrepancy (NWD) that has definite guidance meaning for performing discrimination. Such NWD can be coupled with the classifier to serve as a discriminator satisfying the K-Lipschitz constraint without the requirements of additional weight clipping or gradient penalty strategy. Without bells and whistles, DALN compares favorably against the existing state-of-the-art (SOTA) methods on a variety of public datasets. Moreover, as a plug-and-play technique, NWD can be directly used as a generic regularizer to benefit existing UDA algorithms. Code is available at https://github.com/xiaoachen98/DALN.