Specifically, we find that using the translation probabilities learnt by Model-1 as the cross-lingual similarity function (in place of the commonly-used cosine similarity between word embeddings) performs on-par with state-of-the-art cross-lingual embeddings on word alignment and bilingual dictionary induction tasks.
as long as the similarity function is based on the sentence ID feature space and the embedding/alignment algorithm itself is not too naïve, the actual difference in performance between different approaches is marginal.