Self-conditioning has been central to the success of continuous diffusion language models, as it allows models to correct previous errors. Yet its ability degrades precisely in the regime where diffusion is most attractive for deployment: few-step sampling for fast inference. In this study, we show that when models only have a few denoising steps, inaccurate self-conditioning induces a substantial approximation gap; this mistake compounds across denoising steps and ultimately dominate the sample quality. To address this, we propose a novel training framework that handles these errors during learning by perturbing the self-conditioning signal to match inference noise, improving robustness to prior estimation errors. In addition, we introduce a token-level noise-awareness mechanism that prevents training from saturation, hence improving optimization. Extensive experiments across conditional generation benchmarks demonstrate that our framework surpasses standard continuous diffusion models while providing up to 400x faster inference speed, and remains competitive against other one-step diffusion frameworks.

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.