  Zero-shot translation is a promising direction for building a comprehensive
multilingual neural machine translation (MNMT) system. However, its quality is
still not satisfactory due to off-target issues. In this paper, we aim to
understand and alleviate the off-target issues from the perspective of
uncertainty in zero-shot translation. By carefully examining the translation
output and model confidence, we identify two uncertainties that are responsible
for the off-target issues, namely, extrinsic data uncertainty and intrinsic
model uncertainty. Based on the observations, we propose two light-weight and
complementary approaches to denoise the training data for model training, and
mask out the vocabulary of the off-target languages in inference. Extensive
experiments on both balanced and unbalanced datasets show that our approaches
significantly improve the performance of zero-shot translation over strong MNMT
baselines. Qualitative analyses provide insights into where our approaches
reduce off-target translations
