Corrected Samplers for Discrete Flow Models

2026-01-30

AI Summary

This work addresses the limitations of existing samplers in discrete flow models, which suffer from large discretization errors and high iteration counts due to fixed transition rates, and whose theoretical analyses often rely on strong assumptions about the transition rates or source distributions. For the first time, we establish a general non-asymptotic bound on discretization error without such restrictive assumptions. We further propose two computationally efficient correction-based samplers—time-corrected and position-corrected—with negligible additional overhead; the latter notably reduces iteration complexity. Experiments on both synthetic simulations and text-to-image generation tasks demonstrate that our methods significantly improve sample quality while reducing inference time, confirming their effectiveness and efficiency.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Large language models for search
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

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.

Problem

• discrete flow models
• samplers
• discretization error
• transition rates
• iteration complexity

Innovation

• discrete flow models
• corrected samplers
• discretization error
• iteration complexity
• non-asymptotic bounds