Can Kernel Transfer Operators Help Flow based Generative Models?

Flow-based generative models refer to deep generative models with tractable likelihoods, and offer several attractive properties including efficient density estimation and sampling. Despite many advantages, current formulations (e.g., normalizing flow) often have an expensive memory/runtime footprint, which hinders their use in a number of applications. In this paper, we consider the setting where we have access to an autoencoder, which is suitably effective for the dataset of interest. Under some mild conditions, we show that we can calculate a mapping to a RKHS which subsequently enables deploying mature ideas from the kernel methods literature for flow-based generative models. Specifically, we can explicitly map the RKHS distribution (i.e., approximate the flow) to match or align with a template/well-characterized distribution, via kernel transfer operators. This leads to a direct and resource efficient approximation avoiding iterative optimization. We empirically show that this simple idea yields competitive results on popular datasets such as CelebA, as well as promising results on a public 3D brain imaging dataset where the sample sizes are much smaller.