# Is there any way to train a multi-label machine translation model?

Generally, machine translation is translating a sentence from an original language to a target language. However, for a specific origin sentence, the target sentence is not unique. Now, I have multiple target sentences for a single original sentence. Is there any possible way to train a multi-label machine translation model?

1. Model the conditional distribution $$p(y|x)$$ where $$x$$ is the source sentence and $$y$$ the target.
Under the maximum likelihood framework (which most neural translation models are trained with), (1) simply reduces to finding $$\theta^* = \text{argmax}_\theta \sum_i \log p(y_i|x_i; \theta)$$ where $$(x_i, y_i)$$ are pairs of source and target sentences. But notice this doesn't assume anything about the pairs, including whether each source sentence has only a single corresponding target sentence or not.