  Normalizing flows are powerful non-parametric statistical models that
function as a hybrid between density estimators and generative models. Current
learning algorithms for normalizing flows assume that data points are sampled
independently, an assumption that is frequently violated in practice, which may
lead to erroneous density estimation and data generation. We propose a
likelihood objective of normalizing flows incorporating dependencies between
the data points, for which we derive a flexible and efficient learning
algorithm suitable for different dependency structures. We show that respecting
dependencies between observations can improve empirical results on both
synthetic and real-world data, and leads to higher statistical power in a
downstream application to genome-wide association studies.
