We introduce a novel discriminative latent variable model for bilingual lexicon induction. Our model combines the bipartite matching dictionary prior of Haghighi et al. (2008) with a representation-based approach (Artetxe et al., 2017). To train the model, we derive an efficient Viterbi EM algorithm. We provide empirical results on six language pairs under two metrics and show that the prior improves the induced bilingual lexicons. We also demonstrate how previous work may be viewed as a similarly fashioned latent-variable model, albeit with a different prior.