首次证明离散流匹配模型随数据量增加可逼近真实分布。
A Theoretical Analysis of Discrete Flow Matching Generative Models
- 分解生成误差链，从速度场学习角度分析分布逼近能力。
- 理论证明：训练集越大，生成分布越接近真实分布。
- 适用于关注生成模型理论保障的研究者。
本文对端到端训练的离散流匹配（Discrete Flow Matching, DFM）生成模型进行理论分析。DFM 是一种有前景的离散生成建模框架，通过神经网络近似变换速度场来学习潜在生成动态。我们的分析通过分解最终分布估计误差，建立清晰的保证链条：首先证明生成分布与目标分布之间的总变差距离受学习速度场风险的控制；进而将该风险分解为两个主要来源：(i) 近似误差，量化 Transformer 架构表示真实速度场的能力；(ii) 估计误差，推导出基于有限数据集训练的统计收敛速率。综合上述结果，我们首次提供形式化证明：随着训练集规模增大，训练后的 DFM 模型生成的分布能一致收敛至真实数据分布。
原文摘要 · Abstract (English)
We provide a theoretical analysis for end-to-end training Discrete Flow Matching (DFM) generative models. DFM is a promising discrete generative modeling framework that learns the underlying generative dynamics by training a neural network to approximate the transformative velocity field. Our analysis establishes a clear chain of guarantees by decomposing the final distribution estimation error. We first prove that the total variation distance between the generated and target distributions is controlled by the risk of the learned velocity field. We then bound this risk by analyzing its two primary sources: (i) Approximation Error, where we quantify the capacity of the Transformer architecture to represent the true velocity, and (ii) Estimation Error, where we derive statistical convergence rates that bound the error from training on a finite dataset. By composing these results, we provide the first formal proof that the distribution generated by a trained DFM model provably converges to the true data distribution as the training set size increases.
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