Corpus-based approaches to machine translation rely on the availability of clean parallel corpora. Such resources are scarce, and because of the automatic processes involved in their preparation, they are often noisy. This paper describes an unsupervised method for detecting translation divergences in parallel sentences. We rely on a neural network that computes cross-lingual sentence similarity scores, which are then used to effectively filter out divergent translations. Furthermore, similarity scores predicted by the network are used to identify and fix some partial divergences, yielding additional parallel segments. We evaluate these methods for English-French and English-German machine translation tasks, and show that using filtered/corrected corpora actually improves MT performance.