Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data distribution. This structural restriction greatly accelerates sampling, often enabling high-quality generation with a single Euler step. Under standard assumptions on the neural network classes used to parameterize the velocity field and data distribution, we prove that rectified flows achieve sample complexity $\tilde{O}(\varepsilon^{-2})$. This improves on the best known $O(\varepsilon^{-4})$ bounds for flow matching model and matches the optimal rate for mean estimation. Our analysis exploits the particular structure of rectified flows: because the model is trained with a squared loss along linear paths, the associated hypothesis class admits a sharply controlled localized Rademacher complexity. This yields the improved, order-optimal sample complexity and provides a theoretical explanation for the strong empirical performance of rectified flow models.

翻译：近年来，基于流的生成模型在效率上已展现出优于扩散模型的性能。本文研究修正流模型，该模型将传输轨迹约束为从基分布到数据分布的线性路径。这种结构限制极大加速了采样过程，通常仅需单步欧拉迭代即可实现高质量生成。在用于参数化速度场与数据分布的神经网络类满足标准假设的前提下，我们证明修正流模型达到$\tilde{O}(\varepsilon^{-2})$的样本复杂度。该结果改进了流匹配模型当前已知最优的$O(\varepsilon^{-4})$界，且与均值估计的最优速率相匹配。我们的分析利用了修正流模型的特有结构：由于模型通过沿线性路径的平方损失进行训练，其对应的假设类具有严格可控的局部Rademacher复杂度。这一性质导出了改进的阶最优样本复杂度，并为修正流模型强大的实证性能提供了理论解释。