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.

翻译：得分生成模型（Score-based Generative Models, SGMs）是近年来一类深度生成模型，在众多应用中展现出最先进的性能。本文针对一类通用SGM，在假设得分的精确估计与数据分布为光滑对数凹性的条件下，建立了2-Wasserstein距离下的收敛保证。我们将结果具体应用于若干以随机微分方程建模前向过程的SGM模型，给出了每个模型的迭代复杂度上界，揭示了不同前向过程选择的影响。此外，当数据分布为高斯分布时，我们给出了下界。数值实验方面，我们在CIFAR-10数据集上测试了采用不同前向过程的SGM（其中部分为本文新提出的模型）用于无条件图像生成。实验结果表明，迭代复杂度的实际表现与理论预测高度一致，且采用新提出的前向过程的模型能够超越现有模型。