ReSFlow: One-Step Discrete Data Generation via Rectified Categorical Flows on Statistical Manifolds
Researchers from Inner Mongolia University, Shanghai University of Finance and Economics, and Carnegie Mellon University propose ReSFlow, a method for one-step discrete data generation by rectifying categorical flows on statistical manifolds. The method maps categorical probabilities to a sphere, re-pairs and rectifies generation trajectories, enabling near-geodesic paths with a single model call. Accepted to NeurIPS 2026, ReSFlow achieves quality close to Statistical Flow Matching with 34 calls on binarized MNIST and reduces DNA sequence generation time from 67.94 to 0.409 seconds for 1,000 sequences.
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本文作者分别来自内蒙古大学、上海财经大学和卡内基梅隆大学 (CMU)。第一作者贾啸寰是内蒙古大学博士生，通讯作者为内蒙古大学范少华研究员。上海财经大学的徐韧喆助理教授、王晓副教授以及 CMU 的博士生 Jiayun Wu 为论文的共同作者。 用流匹配（Flow Matching）或扩散模型（Diffusion Models）生成一张手写数字图像、一段 DNA 序列，通常需要从噪声出发，经过多步采样才能得到结果。每一步都要调用模型，生成质量逐渐改善，计算开销也随之增加。 能不能只调用一次模型，就完成整个生成过程？ 对于字符、二值像素和 DNA 碱基等离散数据，难点还在于：类别概率所在的空间具有自己的几何结构，生成路径该如何在这个空间里 “走直”？ 研究团队提出了 Rectified Statistical Flow（ReSFlow）：将类别概率映射到球面，在球面上重新配对并整流生成轨迹，让模型能够沿接近测地线的路径，通过一次更新完成生成。在二值化 MNIST 上，ReSFlow 一次模型调用就获得了接近 Statistical Flow Matching（SFM）34 次调用的生成质量。在条件启动子 DNA 设计任务中，一步采样与完整 ODE 采样的预测活性谱误差接近，生成 1,000 条序列的时间则从 67.94 秒缩短至 0.409 秒。 目前，该工作已经被 NeurIPS 2026 接收。 论文标题： ReSFlow: Rectifying Categorical Flows on Statistical Manifolds for One-Step Generation 论文地址： https://arxiv.org/abs/2610.13225 代码地址： https://github.com/xiaohuanjia/ReSFlow 研究背景 离散数据生成通常从类别概率入手：例如，DNA 中的 A、C、G、T 可以表示为四个非负、和为 1 的概率。模型学习这些概率如何随时间变化，再通过 ODE 推进，最终采样得到离散结果。SFM 引入 Fisher–Rao 几何，用概率空间中的测地线构造训练路径，但要实现一步生成，仍有两个难点。 第一，训练路径是测地线，模型推理时实际走出的路径却未必是。 独立随机配对的条件路径可能在同一时刻交叉，给出不同方向。模型需要综合这
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