Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models

TL;DR

This paper provides theoretical convergence guarantees for a broad class of score-based generative models in Wasserstein distance, analyzing the impact of different forward processes and validating findings with experiments on image generation.

Contribution

It establishes Wasserstein convergence bounds for general SGMs, introduces new forward processes, and links theoretical results with empirical performance.

Findings

Convergence guarantees depend on score estimation accuracy and process smoothness.

New forward processes can outperform existing models in image generation.

Theoretical iteration bounds align with experimental results.

Abstract

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.