Bayesian inference methods are widespread in geophysics and over the decades have been extensively applied to inverse problems, where they are particularly represented through Monte Carlo methods. These are popular as they allow to easily quantify uncertainties and parameter trade-offs but on the downside usually require large computational effort. Here, we propose to use methods from generative deep learning, in particular Normalizing Flows, as global proposal distribution in a Markov chain Monte Carlo context. A simple synthetic example demonstrates that a Normalizing Flow proposal can provide samples with high efficiency and low inter-dependence even in higher dimensions. In a waveform inversion example, it is shown that Normalizing Flows can significantly improve efficiency in sampling complicated posterior distributions. This effect can be increased by adaptive sampling, i.e.\ further refining the Normalizing Flow on its own outputs. The methods presented in this study are thought to be the first application of deep learning-based proposal distributions in geophysics, and contribute to the development of deep-learning enhanced Monte Carlo methods for geophysical inverse problems.