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，融合了生成对抗网络（GAN）高效采样的优点与流模型稳定性能的优势。该模型以特征曲线（characteristics）为驱动，沿这些曲线可将概率密度输运描述为常微分方程（ODEs）。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，生成特征曲线的离散近似序列。随后使用深度神经网络拟合这些特征曲线，确保实现将先验分布有效推向目标分布的一步映射。在理论层面，我们分析了速度匹配、欧拉离散化和特征拟合中的误差，建立了特征生成器在2-瓦瑟斯坦距离下的非渐近收敛速率。据我们所知，这是首个针对免仿真一步生成模型的完整分析。此外，我们的分析改进了现有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该方法，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。