提出ReDi方法，让离散流模型用更少步数生成高质量数据。
ReDi: Rectified Discrete Flow
- 通过修正源与目标分布的耦合关系，降低因子化误差。
- 每步迭代单调减少条件总相关性，实现快速收敛。
- 适用于图像生成，可训练高效单步生成模型。
离散流生成模型（DFM）在高质离散数据生成中表现优异，但通常因依赖多步解码过程导致采样速度慢。本文利用条件总相关性（Conditional TC）分析因子化近似误差，揭示其与耦合关系的依赖性。为此，提出一种新迭代方法ReDi，通过修正源与目标分布的耦合以降低底层因子化误差（以条件TC衡量）。理论上证明每步ReDi均保证条件TC单调下降，确保收敛。实验显示，ReDi显著降低条件TC，支持少步生成。此外，修正后的耦合结构适合训练高效的单步生成模型。ReDi提供了一种简单且理论完备的少步生成方案，为高效离散数据合成提供了新视角。代码见https://github.com/Ugness/ReDi_discrete。
原文摘要 · Abstract (English)
Discrete Flow-based Models (DFMs) are powerful generative models for high-quality discrete data but typically suffer from slow sampling speeds due to their reliance on iterative decoding processes. This reliance on a multi-step process originates from the factorization approximation of DFMs, which is necessary for handling high-dimensional data. In this paper, we analyze the factorization approximation error using Conditional Total Correlation (TC), and reveal its dependence on the coupling. To address the challenge of efficient few-step generation, we propose Rectified Discrete Flow (ReDi), a novel iterative method that reduces the underlying factorization error (measured as Conditional TC) by rectifying the coupling between source and target distributions. We theoretically prove that each ReDi step guarantees a monotonic decreasing Conditional TC, ensuring its convergence. Empirically, ReDi significantly reduces Conditional TC and enables few-step generation. Moreover, we demonstrate that the rectified couplings are well-suited for training efficient one-step models on image generation. ReDi offers a simple and theoretically grounded approach for tackling the few-step challenge, providing a new perspective on efficient discrete data synthesis. Code is available at https://github.com/Ugness/ReDi_discrete.
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