A method and machine translation system for bi-directional translation of textual sequences between a first language and a second language are described. The machine translation system includes a first autoencoder configured to receive a vector representation of a first textual sequence in the first language and encode the vector representation of the first textual sequence into a first sentence embedding. The machine translation system also includes a sum-product network (SPN) configured to receive the first sentence embedding and generate a second sentence embedding by maximizing a first conditional probability of the second sentence embedding given the first sentence embedding and a second autoencoder receiving the second sentence embedding, the second autoencoder being trained to decode the second sentence embedding into a vector representation of a second textual sequence in the second language.