Convergence analysis of OT-Flow for sample generation
Yang Jing Lei Li
Deep generative models aim to learn the underlying distribution of data and
generate new ones. Despite the diversity of generative models and their
high-quality generation performance in practice, most of them lack rigorous
theoretical convergence proofs. In this work, we aim to establish some
convergence results for OT-Flow, one of the deep generative models. First, by
reformulating the framework of OT-Flow model, we establish the
$\Gamma$-convergence of the formulation of OT-flow to the corresponding optimal
transport (OT) problem as the regularization term parameter $\alpha$ goes to
infinity. Second, since the loss function will be approximated by Monte Carlo
method in training, we established the convergence between the discrete loss
function and the continuous one when the sample number $N$ goes to infinity as
well. Meanwhile, the approximation capability of the neural network provides an
upper bound for the discrete loss function of the minimizers. The proofs in
both aspects provide convincing assurances for OT-Flow.