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Deep Metric Learning (DML) has been more attractive and widely applied in many computer vision tasks, in which a discriminative embedding is requested such that the image features belonging to the same class are gathered together and the ones belonging to different classes are pushed apart. Most existing works insist to learn this discriminative embedding by either devising powerful pair-based loss functions or hard-sample mining strategies. However, in this paper, we start from an another perspective and propose Deep Consistent Graph Metric Learning (CGML) framework to enhance the discrimination of the learned embedding. It is mainly achieved by rethinking the conventional distance constraints as a graph regularization and then introducing a Graph Consistency regularization term, which intends to optimize the feature distribution from a global graph perspective. Inspired by the characteristic of our defined ’Discriminative Graph’, which regards DML from another novel perspective, the Graph Consistency regularization term encourages the sub-graphs randomly sampled from the training set to be consistent. We show that our CGML indeed serves as an efficient technique for learning towards discriminative embedding and is applicable to various popular metric objectives, e.g. Triplet, N-Pair and Binomial losses. This paper empirically and experimentally demonstrates the effectiveness of our graph regularization idea, achieving competitive results on the popular CUB, CARS, Stanford Online Products and In-Shop datasets.