Dark matter (DM) is five times more abundant in the Universe than visible matter. Yet, its nature remains unknown and constitutes one of the most exciting and complex research questions today. New astrophysical/experimental big volume and high quality data must be matched with tools that are fit for the complex analysis of these data. Recent developments in deep learning and differentiable programming are likely to play a key role in this regard. Differential programming allows the efficient optimisation of a very large number of parameters of a program, e.g. to choose optimal internal or (astro-)physical parameters of a physical simulation. Deep generative models are Machine Learning programs that can generate data and can be used to simulate physical events. Exploring the optimal use, connection and synergy of these two new possibilities is the main goal of this proposal. We concentrate on two exemplary important datasets for DM research: data from the Large Hadron Collider (LHC), and images of strongly lensed galaxies. We will study how to improve the realism of deep generative models, and connect them with the help of differentiable probabilistic programming techniques to build fast, accurate and flexible new analysis pipelines. We explore the use of these pipelines for anomaly detection (to search for new physics), image and parameter reconstruction. A central outcome of our work will be an accessible and extensible public analysis tool that will spread the best of these new techniques to the large community of DM research and beyond.