Discrete diffusion models have seen a surge of attention with applications on naturally discrete data such as language and graphs. Although discrete-time discrete diffusion has been established for a while, only recently Campbell et al. (2022) introduced the first framework for continuous-time discrete diffusion. However, their training and sampling processes differ significantly from the discrete-time version, necessitating nontrivial approximations for tractability. In this paper, we first present a series of mathematical simplifications of the variational lower bound that enable more accurate and easy-to-optimize training for discrete diffusion. In addition, we derive a simple formulation for backward denoising that enables exact and accelerated sampling, and importantly, an elegant unification of discrete-time and continuous-time discrete diffusion. Thanks to simpler analytical formulations, both forward and now also backward probabilities can flexibly accommodate any noise distribution, including different noise distributions for multi-element objects. Experiments show that our proposed USD3 (for Unified Simplified Discrete Denoising Diffusion) outperform all SOTA baselines on established datasets. We open-source our unified code at https://github.com/LingxiaoShawn/USD3.

提出了一种用于简化离散扩散的数学简化方案，同时还提出了一种能够精确和加速采样的简单公式，并通过创建一个统一的模型，简化离散扩散的前向和后向概率计算，取得了在现有数据集上优于其他方法的效果。

改善和统一的离散和连续时间离散去噪扩散