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.

Influence functions (IFs) are a powerful tool for detecting anomalous examples in large scale datasets. However, they are unstable when applied to deep networks. In this paper, we provide an explanation for the instability of IFs and develop a solution to this problem. We show that IFs are unreliable when the two data points belong to two different classes. Our solution leverages class information to improve the stability of IFs.Extensive experiments show that our modification significantly improves the performance and stability of IFs while incurring no additional computational cost.