1. A speech-to-speech translation system comprising: one or more processors; and memory storing instructions that are executable by the one or more processors, the memory including: an automated speech recognition (ASR) engine to convert audio input in a source language into text output in the source language; a machine translation (MT) engine to receive the text output in the source language from the ASR engine and translate the text output in the source language into text output in a target language that is different than the source language; and a MT training module configured to: model ASR errors of the ASR engine based at least in part on output of the ASR engine to create an ASR simulation model; perform MT to generate training data based at least in part on the ASR simulation model; and train the MT engine using the training data.