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Normalizing flows (NF) use a continuous generator to map a simple latent(e.g. Gaussian) distribution, towards an empirical target distributionassociated with a training data set. Once trained by minimizing a variationalobjective, the learnt map provides an approximate generative model of thetarget distribution. Since standard NF implement differentiable maps, they maysuffer from pathological behaviors when targeting complex distributions. Forinstance, such problems may appear for distributions on multi-componenttopologies or characterized by multiple modes with high probability regionsseparated by very unlikely areas. A typical symptom is the explosion of theJacobian norm of the transformation in very low probability areas. This paperproposes to overcome this issue thanks to a new Markov chain Monte Carloalgorithm to sample from the target distribution in the latent domain beforetransporting it back to the target domain. The approach relies on a Metropolisadjusted Langevin algorithm (MALA) whose dynamics explicitly exploits theJacobian of the transformation. Contrary to alternative approaches, theproposed strategy preserves the tractability of the likelihood and it does notrequire a specific training. Notably, it can be straightforwardly used with anypre-trained NF network, regardless of the architecture. Experiments conductedon synthetic and high-dimensional real data sets illustrate the efficiency ofthe method.

Normalizing flow sampling with Langevin dynamics in the latent space