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Discrete diffusion models have emerged as powerful tools for high-qualitydata generation. Despite their success in discrete spaces, such as textgeneration tasks, the acceleration of discrete diffusion models remainsunder-explored. In this paper, we propose discrete non-Markov diffusion models(DNDM), which naturally induce the predetermined transition time set. Thisenables a training-free sampling algorithm that significantly reduces thenumber of function evaluations (i.e., calls to the neural network), making thesampling process much faster. Furthermore, we study the transition from finiteto infinite step sampling, offering new insights into bridging the gap betweendiscrete and continuous-time processes for discrete diffusion models. Extensiveexperiments on natural language generation and machine translation tasksdemonstrate the superior performance of our method in terms of both generationspeed and sample quality compared to existing methods for discrete diffusionmodels.

Fast Sampling via Discrete Non-Markov Diffusion Models with Predetermined Transition Time