Corrected Samplers for Discrete Flow Models

TL;DR

This paper introduces corrected sampling methods for discrete flow models that significantly reduce discretization errors and improve efficiency without restrictive assumptions, validated through experiments on various tasks.

Contribution

It proposes two corrected samplers, time- and location-corrected, with theoretical error bounds and lower iteration complexity, enhancing discrete flow model sampling.

Findings

Reduced discretization error with corrected samplers

Lower iteration complexity for location-corrected sampler

Improved generation quality and inference speed

Abstract

Discrete flow models (DFMs) have been proposed to learn the data distribution on a finite state space, offering a flexible framework as an alternative to discrete diffusion models. A line of recent work has studied samplers for discrete diffusion models, such as tau-leaping and Euler solver. However, these samplers require a large number of iterations to control discretization error, since the transition rates are frozen in time and evaluated at the initial state within each time interval. Moreover, theoretical results for these samplers often require boundedness conditions of the transition rate or they focus on a specific type of source distributions. To address those limitations, we establish non-asymptotic discretization error bounds for those samplers without any restriction on transition rates and source distributions, under the framework of discrete flow models. Furthermore, by analyzing a one-step lower bound of the Euler sampler, we propose two corrected samplers: \textit{time-corrected sampler} and \textit{location-corrected sampler}, which can reduce the discretization error of tau-leaping and Euler solver with almost no additional computational cost. We rigorously show that the location-corrected sampler has a lower iteration complexity than existing parallel samplers. We validate the effectiveness of the proposed method by demonstrating improved generation quality and reduced inference time on both simulation and text-to-image generation tasks. Code can be found in https://github.com/WanZhengyan/Corrected-Samplers-for-Discrete-Flow-Models.