  Detecting the translation direction of parallel text has applications for
machine translation training and evaluation, but also has forensic applications
such as resolving plagiarism or forgery allegations. In this work, we explore
an unsupervised approach to translation direction detection based on the simple
hypothesis that
$p(\text{translation}|\text{original})>p(\text{original}|\text{translation})$,
motivated by the well-known simplification effect in translationese or
machine-translationese. In experiments with massively multilingual machine
translation models across 20 translation directions, we confirm the
effectiveness of the approach for high-resource language pairs, achieving
document-level accuracies of 82--96% for NMT-produced translations, and 60--81%
for human translations, depending on the model used. Code and demo are
available at https://github.com/ZurichNLP/translation-direction-detection
