arXiv cs.AI· Xiaohuan Jia, Renzhe Xu, Xiao Wang, Jiayun Wu, Shaohua Fan·· 6 天前AI 评分23
ReSFlow：在统计流形上矫正类别流以实现一步生成
ReSFlow: Rectifying Categorical Flows on Statistical Manifolds for One-Step Generation
AI 导读
研究者提出 ReSFlow 模型，通过在统计流形上显式学习遵循内在黎曼几何的测地线轨迹，实现离散数据的一步类别生成。该方法理论上保证先验与目标分布间的轨迹近似测地线，从而大幅降低传输成本，将纯噪声一步映射到目标离散数据。在图像、文本和生物等多个真实生成任务上，ReSFlow 展现出更优的一步生成质量，代码已开源。
正文 · 原文
Abstract:Generative modeling for discrete data has been significantly advanced by learning continuous vector fields on the statistical manifolds to transport simple priors to target discrete distributions. However, because these continuous-time flows are not constrained to follow geodesics on the statistical manifold, thereby requiring multi-step numerical integration for simulation and leading to substantial computational costs during inference. In this work, drawing inspiration from the "straight and fast" properties of Rectified Flow in continuous Euclidean space, we propose the Rectified Statistical Flow (ReSFlow) model, which enables one-step categorical generation on statistical manifolds by explicitly learning geodesic trajectories that adhere to the intrinsic Riemannian geometry. By rectifying the flow on the statistical manifold, we theoretically guarantee that trajectories between prior and target distributions approximate geodesics. This rectification significantly reduces the transport cost by aligning the learned trajectories directly along geodesics on the statistical manifold, allowing the model to map pure noise to target discrete data in a single step. Through extensive experiments on diverse real-world generative tasks, ranging from image and text to biological domains, we demonstrate ReSFlow's superior one-step generation quality, which truly embodies geodesically optimal and rapid categorical generation. Our code is available at this https URL.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.13225 [cs.LG] |
| (or arXiv:2610.13225v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.13225 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Xiaohuan Jia [view email]
[v1]
Fri, 9 Oct 2026 08:44:29 UTC (2,131 KB)
来源：arXiv cs.AI · arxiv.org