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（如扩散模型或流式模型）的概率流直线化是通过数值求解器实现快速采样的关键。现有方法通过直接生成噪声分布与数据分布之间的联合分布概率路径来学习线性路径。基于常微分方程（ODE）求解器模拟这些生成模型时，采样速度慢的一个关键原因是ODE求解器的全局截断误差——ODE轨迹的高曲率导致在低NFE区域中数值求解器的截断误差急剧增大。为解决这一挑战，我们提出名为SeqRF的新型学习方法，通过直线化概率流来降低全局截断误差，从而加速采样并提升合成质量。在理论研究和实验分析中，我们首先验证了SeqRF的直线化特性。通过将SeqRF应用于流式生成模型的实证评估，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。