Cross-lingual natural language processing hinges on the premise that there exists invariance across languages. At the word level, researchers have identified such invariance in the word embedding semantic spaces of different languages. However, in order to connect the separate spaces, cross-lingual supervision encoded in parallel data is typically required. In this paper, we attempt to establish the cross-lingual connection without relying on any cross-lingual supervision. By viewing word embedding spaces as distributions, we propose to minimize their earth mover’s distance, a measure of divergence between distributions. We demonstrate the success on the unsupervised bilingual lexicon induction task. In addition, we reveal an interesting finding that the earth mover’s distance shows potential as a measure of language difference.