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In this paper, we propose an approach that instead expresses the two\nmonolingual embedding spaces as probability densities defined by a Gaussian\nmixture model, and matches the two densities using a method called normalizing\nflow. The method requires no explicit supervision, and can be learned with only\na seed dictionary of words that have identical strings. We argue that this\nformulation has several intuitively attractive properties, particularly with\nthe respect to improving robustness and generalization to mappings between\ndifficult language pairs or word pairs. 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