  This work presents mixed variational flows (MixFlows), a new variational
family that consists of a mixture of repeated applications of a map to an
initial reference distribution. First, we provide efficient algorithms for
i.i.d. sampling, density evaluation, and unbiased ELBO estimation. We then show
that MixFlows have MCMC-like convergence guarantees when the flow map is
ergodic and measure-preserving, and provide bounds on the accumulation of error
for practical implementations where the flow map is approximated. Finally, we
develop an implementation of MixFlows based on uncorrected discretized
Hamiltonian dynamics combined with deterministic momentum refreshment.
Simulated and real data experiments show that MixFlows can provide more
reliable posterior approximations than several black-box normalizing flows, as
well as samples of comparable quality to those obtained from state-of-the-art
MCMC methods.
