  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.
