Abstract
Generative Adversarial Networks (GANs) require the calculation of a saddle point through a sequence of minimization and maximization steps, which leads to numerical instabilities. Numerous numerical variants have been developed, but these algorithms tend to memorize the original data rather than generalize, which significantly limits their applications.
An alternative approach using invertible transports has been developed. Just like GANs, the transport is applied to data that is a realization of Gaussian white noise. This data is progressively transformed by a sequence of parameterized diffeomorphisms. This defines an invertible transport. The parameters are optimized by maximizing the likelihood of the transported distribution, which is equivalent to minimizing the Kullback-Leibler distance between the transported distribution and that of the data.
