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Non-autoregressive transformers (NATs) predict entire sequences in parallel to reduce decoding latency, but they often encounter performance challenges due to the multi-modality problem. A recent advancement, the Directed Acyclic Transformer (DAT), addresses this issue by capturing multiple translation modalities to paths in a Directed Acyclic Graph (DAG). However, the collaboration with the latent variable introduced through the Glancing training (GLAT) is crucial for DAT to attain state-of-the-art performance. In this paper, we introduce Diffusion Directed Acyclic Transformer (Diff-DAT), which serves as an alternative to GLAT as a latent variable introduction for DAT. Diff-DAT offers two significant benefits over the previous approach. Firstly, it establishes a stronger alignment between training and inference. Secondly, it facilitates a more flexible tradeoff between quality and latency.