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 discrete non-Markov diffusion models (DNDM), which naturally induce the predetermined transition time set. This enables a training-free sampling algorithm that 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。尽管在文本生成等离散空间任务中取得了成功，离散扩散模型的加速研究仍显不足。本文提出离散非马尔可夫扩散模型（DNDM），其自然诱导出预定转移时间集。这实现了一种免训练的采样算法，可显著减少函数评估次数（即神经网络调用），大幅提升采样速度。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的衔接提供了新见解。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表现出优越性能。