修正CondOT：高斯流匹配中的精确有限步采样
Correcting CondOT: Exact Finite-Step Sampling in Gaussian Flow Matching
查看机构详情
- Technion（以色列理工学院）
机构由 AI 辅助整理，请以论文原文为准。
浏览论文内容
中文总结 AI 辅助
本文研究高斯流匹配中有限步采样的误差，证明标准CondOT调度可消除主要中点误差，并构造以1/S速率逼近其噪声调度的调度以实现精确采样。
中文摘要 AI 辅助
流匹配通过逐步将噪声转化为数据来生成样本。在实践中，使用有限数量的采样步会引入数值误差，该误差取决于所选择的调度。我们针对高斯目标和显式中点采样方法，使用精确流场研究这种依赖性。我们通过目标分布与中点采样器产生的最终分布之间的平方Wasserstein距离来衡量采样误差。我们证明，标准的条件最优传输（CondOT）调度能够消除主要的中点误差，并改进一般的收敛界，即使采样步长不相等时也是如此。在S个采样步的均匀网格上，我们将信号调度固定为α_t=t，并证明存在标量噪声调度β_t，其以1/S的速率逼近CondOT噪声调度1-t，并为每个足够大的S产生精确的高斯采样。受控的高斯实验说明了收敛速率和精确校准。
英文摘要
Flow matching generates samples by gradually transforming noise into data. In practice, using a finite number of sampling steps introduces a numerical error that depends on the chosen schedule. We study this dependence for Gaussian targets and the explicit midpoint sampling method, using the exact flow field. We measure sampling error by the squared Wasserstein distance between the target distribution and the final distribution produced by the midpoint sampler. We show that the standard conditional optimal transport (CondOT) schedule cancels the leading midpoint error and improves the general convergence bound, even when the sampling steps are unequally spaced. On a uniform grid of $S$ sampling steps, we fix the signal schedule at $α_t=t$ and prove the existence of scalar noise schedules $β_t$ that approach the CondOT noise schedule $1-t$ at rate $1/S$ and yield exact Gaussian sampling for every sufficiently large $S$. Controlled Gaussian experiments illustrate the convergence rates and exact calibration.
