arXiv：cs.LG· Hari Krishna Sahoo, Mudit Gaur, Vaneet Aggarwal·· 4 小时前AI 评分43
Rectified Flows 的阶最优样本复杂度
Order-Optimal Sample Complexity of Rectified Flows
AI 导读
研究证明，约束传输轨迹为线性的 Rectified Flows 模型可达到 Õ(ε⁻²) 的样本复杂度，优于 Flow Matching 模型已知最佳的 O(ε⁻⁴) 界，并匹配均值估计的最优速率。分析利用线性路径上平方损失训练带来的局部化 Rademacher 复杂度，为该模型在单步 Euler 采样下仍具高质量生成能力提供了理论解释。
正文
Abstract: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.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Information Theory (cs.IT); Machine Learning (stat.ML) |
| Cite as: | arXiv:2601.20250 [cs.LG] |
| (or arXiv:2601.20250v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2601.20250 arXiv-issued DOI via DataCite |
Submission history
From: Hari Krishna Sahoo [view email]
[v1]
Wed, 28 Jan 2026 04:55:14 UTC (62 KB)
[v2]
Tue, 6 Oct 2026 19:22:42 UTC (589 KB)
来源：arXiv：cs.LG · arxiv.org