  Non-autoregressive translation (NAT) models achieve comparable performance
and superior speed compared to auto-regressive translation (AT) models in the
context of sentence-level machine translation (MT). However, their abilities
are unexplored in document-level MT, hindering their usage in real scenarios.
In this paper, we conduct a comprehensive examination of typical NAT models in
the context of document-level MT and further propose a simple but effective
design of sentence alignment between source and target. Experiments show that
NAT models achieve high acceleration on documents, and sentence alignment
significantly enhances their performance.
  However, current NAT models still have a significant performance gap compared
to their AT counterparts. Further investigation reveals that NAT models suffer
more from the multi-modality and misalignment issues in the context of
document-level MT, and current NAT models struggle with exploiting document
context and handling discourse phenomena. We delve into these challenges and
provide our code at \url{https://github.com/baoguangsheng/nat-on-doc}.
