Supervised person re-identification (ReID) often has poor scalability and usability in real-world deployments due to domain gaps and the lack of annotations for the target domain data. Unsupervised person ReID through domain adaptation is attractive yet challenging. Existing unsupervised ReID approaches often fail in correctly identifying the positive samples and negative samples through the distance-based matching/ranking. The two distributions of distances for positive sample pairs

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... and negative sample pairs (Neg-distr) are often not well separated, having large overlap. To address this problem, we introduce a global distance-distributions separation (GDS) constraint over the two distributions to encourage the clear separation of positive and negative samples from a global view. We model the two global distance distributions as Gaussian distributions and push apart the two distributions while encouraging their sharpness in the unsupervised training process. Particularly, to model the distributions from a global view and facilitate the timely updating of the distributions and the GDS related losses, we leverage a momentum update mechanism for building and maintaining the distribution parameters (mean and variance) and calculate the loss on the fly during the training. Distribution-based hard mining is proposed to further promote the separation of the two distributions. We validate the effectiveness of the GDS constraint in unsupervised ReID networks. Extensive experiments on multiple ReID benchmark datasets show our method leads to significant improvement over the baselines and achieves the state-of-the-art performance.