  Resolving semantic ambiguity has long been recognised as a central challenge
in the field of Machine Translation. Recent work on benchmarking translation
performance on ambiguous sentences has exposed the limitations of conventional
Neural Machine Translation (NMT) systems, which fail to handle many such cases.
Large language models (LLMs) have emerged as a promising alternative,
demonstrating comparable performance to traditional NMT models while
introducing new paradigms for controlling the target outputs. In this paper, we
study the capabilities of LLMs to translate "ambiguous sentences" - i.e. those
containing highly polysemous words and/or rare word senses. We also propose two
ways to improve their disambiguation capabilities, through a) in-context
learning and b) fine-tuning on carefully curated ambiguous datasets.
Experiments show that our methods can match or outperform state-of-the-art
systems such as DeepL and NLLB in four out of five language directions. Our
research provides valuable insights into effectively adapting LLMs to become
better disambiguators during Machine Translation. We release our curated
disambiguation corpora and resources at
https://data.statmt.org/ambiguous-europarl.
