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：我们提出了一种新颖的一步生成模型——特征生成器，它结合了生成对抗网络（GANs）的采样效率和基于流的模型的稳定性能。我们的模型由特征驱动，沿着这些特征，概率密度输运可以用常微分方程（ODEs）来描述。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，从而生成一系列对特征的离散逼近。然后，我们使用深度神经网络来拟合这些特征，确保一个一步映射能够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、欧拉离散化和特征拟合中的误差，从而为特征生成器在2-Wasserstein距离上建立了一个非渐近收敛速率。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。我们在合成数据集和真实数据集上应用了我们的方法，结果表明，特征生成器仅需对神经网络进行一次评估即可实现高质量的生成。