Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and employed in practice, the theoretical understandings about convergence properties of the probability flow ODE are still quite limited. In this paper, we provide the first non-asymptotic convergence analysis for a general class of probability flow ODE samplers in 2-Wasserstein distance, assuming accurate score estimates. We then consider various examples and establish results on the iteration complexity of the corresponding ODE-based samplers.

翻译：基于概率流常微分方程的分数生成建模已在多种应用中取得显著成功。尽管文献中已提出多种快速ODE采样器并应用于实践，但关于概率流ODE收敛性质的理论理解仍相当有限。本文首次针对一般类别的概率流ODE采样器，在假设分数估计精确的前提下，给出了2-Wasserstein距离下的非渐近收敛性分析。随后，我们考察了多个实例，并建立了相应ODE采样器的迭代复杂度结果。