提出低维适应的修正流采样方法，加速生成过程。
Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspective
- 设计新时间离散方案，利用目标分布内在维度提升采样效率。
- 理论证明迭代复杂度达 O(k/ε)，优于传统方法，其中 k 为内在维度。
- 连接扩散模型与随机局部化，实现更鲁棒的低维自适应采样。
近年来，修正流（Rectified Flow, RF）因其生成效率和顶尖性能广受关注。本文研究了RF在多大程度上能自动适应目标分布支撑集的内在低维性以加速采样。结果表明，在精心设计的时间离散方案与足够精确的漂移估计下，RF采样器的迭代复杂度可达 $O(k/\varepsilon)$（含对数因子），其中 $\varepsilon$ 为总变差距离精度，$k$ 为目标分布的内在维度。此外，本文揭示了去噪扩散概率模型（DDPM）与随机版本的修正流之间的等价关系，并建立其与随机局部化的全新联系。基于此，进一步设计了一种新的随机修正流采样器，在对漂移估计精度要求更低且特定时间调度下仍能实现对目标分布低维性的自适应。通过合成数据和文生图实验验证，新设计的时间离散方案显著提升了采样性能。
原文摘要 · Abstract (English)
In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the degree to which RF automatically adapts to the intrinsic low dimensionality of the support of the target distribution to accelerate sampling. We show that, using a carefully designed choice of the time-discretization scheme and with sufficiently accurate drift estimates, the RF sampler enjoys an iteration complexity of order $O(k/\varepsilon)$ (up to log factors), where $\varepsilon$ is the precision in total variation distance and $k$ is the intrinsic dimension of the target distribution. In addition, we show that the denoising diffusion probabilistic model (DDPM) procedure is equivalent to a stochastic version of RF by establishing a novel connection between these processes and stochastic localization. Building on this connection, we further design a stochastic RF sampler that also adapts to the low-dimensionality of the target distribution under milder requirements on the accuracy of the drift estimates, and also with a specific time schedule. We illustrate with simulations on the synthetic data and text-to-image data experiments the improved performance of the proposed samplers implementing the newly designed time-discretization schedules.
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