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We study a normalizing flow in the latent space of a top-down generatormodel, in which the normalizing flow model plays the role of the informativeprior model of the generator. We propose to jointly learn the latent spacenormalizing flow prior model and the top-down generator model by a Markov chainMonte Carlo (MCMC)-based maximum likelihood algorithm, where a short-runLangevin sampling from the intractable posterior distribution is performed toinfer the latent variables for each observed example, so that the parameters ofthe normalizing flow prior and the generator can be updated with the inferredlatent variables. We show that, under the scenario of non-convergent short-runMCMC, the finite step Langevin dynamics is a flow-like approximate inferencemodel and the learning objective actually follows the perturbation of themaximum likelihood estimation (MLE). We further point out that the learningframework seeks to (i) match the latent space normalizing flow and theaggregated posterior produced by the short-run Langevin flow, and (ii) bias themodel from MLE such that the short-run Langevin flow inference is close to thetrue posterior. Empirical results of extensive experiments validate theeffectiveness of the proposed latent space normalizing flow model in the tasksof image generation, image reconstruction, anomaly detection, supervised imageinpainting and unsupervised image recovery.

A Tale of Two Latent Flows: Learning Latent Space Normalizing Flow with Short-run Langevin Flow for Approximate Inference