Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on large-scale datasets, numerical simulation requires multiple evaluations of a neural network, leading to a slow sampling speed. We attribute the reason to the high curvature of the learned generative trajectories, as it is directly related to the truncation error of a numerical solver. Based on the relationship between the forward process and the curvature, here we present an efficient method of training the forward process to minimize the curvature of generative trajectories without any ODE/SDE simulation. Experiments show that our method achieves a lower curvature than previous models and, therefore, decreased sampling costs while maintaining competitive performance. Code is available at https://github.com/sangyun884/fast-ode.

翻译：近期基于常微分方程/随机微分方程的生成模型，例如扩散模型、整流流和流匹配，将生成过程定义为固定前向过程的时间反转。尽管这些模型在大型数据集上展现出卓越性能，但数值模拟需要多次评估神经网络，导致采样速度缓慢。我们将此归因于学习到的生成轨迹的高曲率，因为它与数值求解器的截断误差直接相关。基于前向过程与曲率之间的关系，本文提出了一种高效方法，无需任何ODE/SDE模拟即可训练前向过程以最小化生成轨迹的曲率。实验表明，我们的方法比先前模型实现了更低的曲率，从而在保持竞争力性能的同时降低了采样成本。代码见 https://github.com/sangyun884/fast-ode。