发表机构
Cherkasy State Technological University（切尔卡瑟国立技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究提出速度调度流匹配（VSFM）方法，放宽流匹配中样本恒速移动的隐含选择。通过特定多项式轮廓，预训练模型推理时无需重新训练和额外计算，FID降低，从零开始训练也有进一步提升，增益源于欧拉积分器局部截断误差。
AI 中文摘要
流匹配训练神经网络以沿噪声与数据之间的线性插值回归条件速度，网络评估次数（NFE）决定采样成本。直线插值有隐含选择：样本在整个轨迹以恒定速度移动。我们放宽此选择，引入速度调度流匹配（VSFM），用\(v(t)(x_1 - x_0)\)取代条件目标\(x_1 - x_0\)。研究了六种来自运动规划的多项式轮廓。VSFM首次用于推理时：预训练的线性流匹配模型可通过在非均匀\(\tau\)调度上积分其常微分方程，在任何允许轮廓下采样，无需重新训练和额外计算，在CIFAR - 10上FID降低达\(19.8\%\)。从零开始在制动轮廓下训练，在4次NFE时进一步降低\(17.4\%\)。这些增益源于欧拉积分器在诱导网格上的局部截断误差。
英文摘要
Flow matching trains a neural network to regress the conditional velocity along a linear interpolant between noise and data, and the number of network evaluations~(NFE) sets the cost of sampling. The straight-line interpolant carries an implicit choice: the sample moves at constant speed throughout the trajectory. We relax this choice and introduce Velocity Scheduled Flow Matching~(VSFM), which replaces the conditional target $x_1 - x_0$ with $v(t)(x_1 - x_0)$ for any nonnegative profile $v:[0,1]\to\mathbb{R}_{\geq 0}$ satisfying $\int_0^1 v\,dt = 1$. We study six polynomial profiles drawn from motion planning. The first use of VSFM is at inference time: a pretrained linear flow-matching model can be sampled under any admissible profile by integrating its ODE on a non-uniform $τ$-schedule, with no retraining and no additional computation; on CIFAR-10 this lowers FID by up to $19.8\%$. Training from scratch under a braking profile gives a further reduction of $17.4\%$ at $4$~NFE. Both gains follow from the local truncation error of the Euler integrator on the induced grid.
