Ordinary differential equation (ODE) based generative models have emerged as a powerful approach for producing high-quality samples in many applications. However, the ODE-based methods either suffer the discretization error of numerical solvers of ODE, which restricts the quality of samples when only a few NFEs are used, or struggle with training instability. In this paper, we proposed Integration Flow, which directly learns the integral of ODE-based trajectory paths without solving the ODE functions. Moreover, Integration Flow explicitly incorporates the target state $\mathbf{x}_0$ as the anchor state in guiding the reverse-time dynamics. We have theoretically proven this can contribute to both stability and accuracy. To the best of our knowledge, Integration Flow is the first model with a unified structure to estimate ODE-based generative models and the first to show the exact straightness of 1-Rectified Flow without reflow. Through theoretical analysis and empirical evaluations, we show that Integration Flows achieve improved performance when it is applied to existing ODE-based models, such as diffusion models, Rectified Flows, and PFGM++. Specifically, Integration Flow achieves one-step generation on CIFAR10 with FIDs of 2.86 for the Variance Exploding (VE) diffusion model, 3.36 for rectified flow without reflow, and 2.91 for PFGM++; and on ImageNet with FIDs of 4.09 for VE diffusion model, 4.35 for rectified flow without reflow and 4.15 for PFGM++.

该研究针对传统ODE生成模型在样本质量和训练稳定性方面的不足，提出了一种新的“集成流”方法。该方法直接学习ODE轨迹路径的积分，避免了解析ODE函数的需求，并通过理论证明提升了模型的稳定性和准确性。集成流在多个现有ODE基础模型中表现出更优的性能，显示了其在生成模型领域的潜在影响。

集成流模型