We propose the characteristic generator, a novel one-step generative model that combines the efficiency of sampling in Generative Adversarial Networks (GANs) with the stable performance of flow-based models. Our model is driven by characteristics, along which the probability density transport can be described by ordinary differential equations (ODEs). Specifically, We estimate the velocity field through nonparametric regression and utilize Euler method to solve the probability flow ODE, generating a series of discrete approximations to the characteristics. We then use a deep neural network to fit these characteristics, ensuring a one-step mapping that effectively pushes the prior distribution towards the target distribution. In the theoretical aspect, we analyze the errors in velocity matching, Euler discretization, and characteristic fitting to establish a non-asymptotic convergence rate for the characteristic generator in 2-Wasserstein distance. To the best of our knowledge, this is the first thorough analysis for simulation-free one step generative models. Additionally, our analysis refines the error analysis of flow-based generative models in prior works. We apply our method on both synthetic and real datasets, and the results demonstrate that the characteristic generator achieves high generation quality with just a single evaluation of neural network.

翻译：我们提出特征生成器（characteristic generator），这是一种新颖的一步生成模型，它将生成对抗网络（GANs）的采样效率与基于流的模型的稳定性能相结合。我们的模型由特征线驱动，沿这些特征线的概率密度输运可由常微分方程（ODEs）描述。具体而言，我们通过非参数回归估计速度场，并利用欧拉方法求解概率流ODE，从而生成特征线的一系列离散近似。随后，我们使用深度神经网络拟合这些特征线，确保实现一步映射，有效地将先验分布推向目标分布。在理论方面，我们分析了速度匹配、欧拉离散化及特征拟合中的误差，建立了特征生成器在2-Wasserstein距离下的非渐近收敛率。据我们所知，这是对免模拟一步生成模型的首次全面分析。此外，我们的分析改进了先前工作中基于流的生成模型的误差分析。我们将该方法应用于合成数据集和真实数据集，结果表明，特征生成器仅需单次神经网络评估即可实现高质量生成。