Score-based generative models (SGMs) is a recent class of deep generative models with state-of-the-art performance in many applications. In this paper, we establish convergence guarantees for a general class of SGMs in 2-Wasserstein distance, assuming accurate score estimates and smooth log-concave data distribution. We specialize our result to several concrete SGMs with specific choices of forward processes modelled by stochastic differential equations, and obtain an upper bound on the iteration complexity for each model, which demonstrates the impacts of different choices of the forward processes. We also provide a lower bound when the data distribution is Gaussian. Numerically, we experiment SGMs with different forward processes, some of which are newly proposed in this paper, for unconditional image generation on CIFAR-10. We find that the experimental results are in good agreement with our theoretical predictions on the iteration complexity, and the models with our newly proposed forward processes can outperform existing models.

在本研究中，我们针对具有最先进性能的分数生成模型（SGMs）这一最新类别的深度生成模型，基于确切的评分估计和平滑的对数凹分布假设，在2-Wasserstein距离上提出了收敛性保证。我们针对几种具体的SGM模型将结果特化，这些模型采用了由随机微分方程建模的前向过程的特定选择，并获得了每个模型的迭代复杂度的上界，从而展示了不同前向过程选择的影响。当数据分布为高斯分布时，我们还提供了一个下界。在数值上，我们使用不同前向过程的SGMs进行CIFAR-10的无条件图像生成实验。我们发现实验结果与我们关于迭代复杂度的理论预测非常吻合，并且具有我们新提出的前向过程的模型可以胜过现有模型。

一类基于评分的生成模型的Wasserstein收敛保证