Convergence Analysis for General Probability Flow ODEs of Diffusion
  Models in Wasserstein Distances
Xuefeng Gao Lingjiong Zhu
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.