Abstract In this work, we connect two distinct concepts for unsupervised domain adaptation: feature distribution alignment between domains by utilizing the task-specifific decision boundary [57] and the Wasserstein metric [72]. Our proposed sliced Wasserstein discrepancy (SWD) is designed to capture the natural notion of dissimilarity between the outputs of task-specifific classififiers. It provides a geometrically meaningful guidance to detect target samples that are far from the support of the source and enables effificient distribution alignment in an end-to-end trainable fashion. In the experiments, we validate the effectiveness and genericness of our method on digit and sign recognition, image classififi- cation, semantic segmentation, and object detection