Variational inference is a popular approach for approximate Bayesian inference that is particulary promising for highly parameterized models such as deep neural networks. A key challenge of variational inference is to approximate the posterior over model parameters with a distribution that is simpler and tractable yet sufficiently expressive. In this work, we propose a method for training highly flexible variational distributions by starting with a coarse approximation and iteratively refining it. Each refinement step makes cheap, local adjustments and only requires optimization of simple variational families. We demonstrate theoretically that our method always improves a bound on the approximation (the Evidence Lower BOund) and observe this empirically across a variety of benchmark tasks. In experiments, our method consistently outperforms recent variational inference methods for deep learning in terms of log-likelihood and the ELBO.