Discrete diffusion models have emerged as powerful tools for high-quality data generation. Despite their success in discrete spaces, such as text generation tasks, the acceleration of discrete diffusion models remains under explored. In this paper, we propose a discrete non-Markov diffusion model, which admits an accelerated reverse sampling for discrete data generation. Our method significantly reduces the number of function evaluations (i.e., calls to the neural network), making the sampling process much faster. Furthermore, we study the transition from finite to infinite step sampling, offering new insights into bridging the gap between discrete and continuous-time processes for discrete diffusion models. Extensive experiments on natural language generation and machine translation tasks demonstrate the superior performance of our method in terms of both generation speed and sample quality compared to existing methods for discrete diffusion models.

翻译：离散扩散模型已成为高质量数据生成的强大工具。尽管其在离散空间（如文本生成任务）中取得了成功，离散扩散模型的加速研究仍显不足。本文提出一种离散非马尔可夫扩散模型，该模型支持针对离散数据生成的加速逆向采样。我们的方法显著减少了函数评估次数（即神经网络调用次数），使采样过程大幅加速。此外，我们研究了从有限步到无限步采样的过渡，为离散扩散模型中离散与连续时间过程之间的鸿沟提供了新的理论洞见。在自然语言生成和机器翻译任务上的大量实验表明，相较于现有离散扩散模型方法，我们的方法在生成速度与样本质量方面均展现出优越性能。