Straightening the probability flow of the continuous-time generative models, such as diffusion models or flow-based models, is the key to fast sampling through the numerical solvers, existing methods learn a linear path by directly generating the probability path the joint distribution between the noise and data distribution. One key reason for the slow sampling speed of the ODE-based solvers that simulate these generative models is the global truncation error of the ODE solver, caused by the high curvature of the ODE trajectory, which explodes the truncation error of the numerical solvers in the low-NFE regime. To address this challenge, We propose a novel method called SeqRF, a learning technique that straightens the probability flow to reduce the global truncation error and hence enable acceleration of sampling and improve the synthesis quality. In both theoretical and empirical studies, we first observe the straightening property of our SeqRF. Through empirical evaluations via SeqRF over flow-based generative models, We achieve surpassing results on CIFAR-10, CelebA-$64 \times 64$, and LSUN-Church datasets.

翻译：连续时间生成模型（如扩散模型或基于流的模型）的概率流拉直是实现数值求解器快速采样的关键。现有方法通过直接生成噪声与数据分布之间的联合分布对应的概率路径来学习线性路径。基于常微分方程(ODE)的求解器模拟这些生成模型时采样速度缓慢的一个关键原因在于ODE求解器的全局截断误差——由于ODE轨迹的高曲率，导致在低NFE（函数评估次数）区间内数值求解器的截断误差急剧扩大。为应对这一挑战，我们提出名为SeqRF的新方法，这是一种通过拉直概率流来降低全局截断误差的学习技术，从而加速采样并提升合成质量。在理论与实验研究中，我们首先观察到SeqRF的拉直特性。通过在基于流的生成模型上对SeqRF进行实证评估，我们在CIFAR-10、CelebA-$64 \times 64$和LSUN-Church数据集上取得了超越现有方法的结果。