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[2601.15500] Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspective
Summary
This paper explores the adaptation of Rectified Flow (RF) to low-dimensional target distributions, demonstrating improved sampling efficiency through innovative time-discretization techniques and connections to denoising diffusion models.
Why It Matters
Understanding how RF can adapt to low-dimensional distributions is crucial for enhancing sampling efficiency in machine learning applications. This research provides insights that could lead to more effective algorithms in generative modeling and statistical inference, impacting various fields such as AI and data science.
Key Takeaways
- RF can adapt to the intrinsic low dimensionality of target distributions, improving sampling efficiency.
- The paper establishes a novel connection between RF and denoising diffusion probabilistic models.
- A new stochastic RF sampler is proposed that requires less accuracy in drift estimates.
- Simulations demonstrate the effectiveness of the new time-discretization schedules.
- The findings could influence future developments in generative modeling techniques.
Statistics > Machine Learning arXiv:2601.15500 (stat) [Submitted on 21 Jan 2026 (v1), last revised 20 Feb 2026 (this version, v3)] Title:Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspective Authors:Saptarshi Roy, Alessandro Rinaldo, Purnamrita Sarkar View a PDF of the paper titled Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspective, by Saptarshi Roy and 2 other authors View PDF HTML (experimental) Abstract: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-di...
