Corrected Samplers for Discrete Flow Models

Researchers have proposed two corrected sampling methods for discrete flow models that reduce discretization error with almost no additional computational cost, according to a paper revised in May 2026 [1]. Discrete flow models learn data distributions on finite state spaces and serve as an alternative to discrete diffusion models [1]. Existing samplers such as tau-leaping and the Euler solver require many iterations to control discretization error because transition rates are frozen in time and evaluated only at the initial state within each interval [1]. Theoretical guarantees for those samplers have often required boundedness conditions on the transition rate or have been restricted to specific source distributions [1]. To address these constraints, the authors establish non-asymptotic discretization error bounds that apply without any restriction on transition rates or source distributions [1]. By analyzing a one-step lower bound of the Euler sampler, they introduce two corrected samplers: a time-corrected sampler and a location-corrected sampler [1]. Both are designed to reduce the discretization error of tau-leaping and Euler solvers while adding almost no computational overhead [1]. The location-corrected sampler is shown to have lower complexity than existing parallel samplers [1]. Sampling quality is a central concern across computational statistics. Monte Carlo methods, which rely on repeated random sampling to obtain numerical results, are widely used for optimization, numerical integration, and non-uniform random variate generation [3]. Assessing the quality of such samplers has led to tools such as the Stein discrepancy, a statistical divergence rooted in Stein’s method that was first formulated to evaluate Markov chain Monte Carlo samplers and has since been adopted in machine learning and computer science [5]. The corrected samplers were validated on simulations and text-to-image generation tasks, where they achieved better generation quality with reduced inference time [1]. The paper, authored by Zhengyan Wan, was first submitted on 30 January 2026 and last revised on 26 May 2026 [1]. Code for the methods is publicly available on GitHub [1].