Related papers: Order-Optimal Sample Complexity of Rectified Flows

Order-Optimal Sample Complexity of Rectified Flows

URL: http://arxiv.org/abs/2601.20250v1
Date: Wed, 28 Jan 2026 04:55:14 GMT
Title: Order-Optimal Sample Complexity of Rectified Flows
Authors: Hari Krishna Sahoo, Mudit Gaur, Vaneet Aggarwal,
Abstract summary: We study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data distribution.<n>This structural restriction greatly accelerates sampling, often enabling high-quality generation with a single step.
Score: 43.61958734990224
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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