  Non-autoregressive translation (NAT) reduces the decoding latency but suffers
from performance degradation due to the multi-modality problem. Recently, the
structure of directed acyclic graph has achieved great success in NAT, which
tackles the multi-modality problem by introducing dependency between vertices.
However, training it with negative log-likelihood loss implicitly requires a
strict alignment between reference tokens and vertices, weakening its ability
to handle multiple translation modalities. In this paper, we hold the view that
all paths in the graph are fuzzily aligned with the reference sentence. We do
not require the exact alignment but train the model to maximize a fuzzy
alignment score between the graph and reference, which takes captured
translations in all modalities into account. Extensive experiments on major WMT
benchmarks show that our method substantially improves translation performance
and increases prediction confidence, setting a new state of the art for NAT on
the raw training data.
