  We present a method for conditional sampling for pre-trained normalizing
flows when only part of an observation is available. We derive a lower bound to
the conditioning variable log-probability using Schur complement properties in
the spirit of Gaussian conditional sampling. Our derivation relies on
partitioning flow's domain in such a way that the flow restrictions to
subdomains remain bijective, which is crucial for the Schur complement
application. Simulation from the variational conditional flow then amends to
solving an equality constraint. Our contribution is three-fold: a) we provide
detailed insights on the choice of variational distributions; b) we discuss how
to partition the input space of the flow to preserve bijectivity property; c)
we propose a set of methods to optimise the variational distribution. Our
numerical results indicate that our sampling method can be successfully applied
to invertible residual networks for inference and classification.
