- Convergence analysis of general stochastic flow ODE of diffusion model at Wasserstein distance (arXiv)
Author: Xuefeng Gao, Lingjiong Zhu
Abstract: : Score-based generative modeling using stochastic flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. Although various fast ODE-based samplers have been proposed in the literature and used in practice, the theoretical understanding of the convergence properties of stochastic flow ODEs is still quite limited. In this paper, we provide the first non-asymptotic convergence analysis for the general class of stochastic flow ODE samplers at the 2-Wasserstein distance, assuming accurate score estimation. Next, we consider various examples and establish corresponding results regarding the iteration complexity of his ODE-based sampler.
2. Formulation of discrete stochastic flow with optimal transport (arXiv)
Author: Pengze Zhang, Hubery ying, Chen Li, Xiaohua Xie
Summary: It is generally accepted that continuous diffusion models display deterministic stochastic flows, whereas discrete diffusion models do not. This paper aims to establish the basic theory of stochastic flows in discrete diffusion models. Specifically, we first prove that continuous stochastic flows are Monge-optimal transport maps under certain conditions, and provide comparable evidence for the discrete case. Considering these findings, we can define discrete stochastic flows along the principles of optimal transport. Finally, we utilize our newly established definitions to propose a new sampling method that exceeds previous discrete diffusion models in its ability to produce more robust results. Extensive experiments on synthetic toy dataset and CIFAR-10 dataset validate the effectiveness of the proposed discrete stochastic flow. The code is released at https://github.com/PangzeCheung/Discrete-Probability-Flow.
