Wasserstein Convergence Guarantees for a General Class of Score-Based
  Generative Models
Xuefeng Gao Hoang M. Nguyen Lingjiong Zhu
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.