Recent ODE/SDE-based generative models, such as diffusion models 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（如扩散模型和流匹配）将生成过程定义为固定前向过程的时间反转。尽管这类模型在大规模数据集上展现出卓越性能，但数值模拟需要对神经网络进行多次评估，导致采样速度缓慢。我们认为其原因在于学习到的生成轨迹具有高曲率——这直接关系到数值求解器的截断误差。基于前向过程与曲率之间的关系，本文提出一种高效训练前向过程的方法，可在无需任何常微分方程/随机微分方程模拟的情况下最小化生成轨迹的曲率。实验表明，与现有模型相比，我们的方法在保持竞争性能的同时实现了更低曲率，从而降低了采样成本。代码开源地址：https://github.com/sangyun884/fast-ode