  Fueled by the expressive power of deep neural networks, normalizing flows
have achieved spectacular success in generative modeling, or learning to draw
new samples from a distribution given a finite dataset of training samples.
Normalizing flows have also been applied successfully to variational inference,
wherein one attempts to learn a sampler based on an expression for the
log-likelihood or energy function of the distribution, rather than on data. In
variational inference, the unimodality of the reference Gaussian distribution
used within the normalizing flow can cause difficulties in learning multimodal
distributions. We introduce an extension of normalizing flows in which the
Gaussian reference is replaced with a reference distribution that is
constructed via a tensor network, specifically a matrix product state or tensor
train. We show that by combining flows with tensor networks on difficult
variational inference tasks, we can improve on the results obtained by using
either tool without the other.
