The next several years will witness an influx of astrophysical data that will enable us to accurately map out the distribution of matter in the Universe, image billions of stars and galaxies to unprecedented precision, and create the highest-resolution maps of the Milky Way to-date. These observations may contain signatures of new physics beyond the Standard Models of particle physics and cosmology, including hints about the nature of dark matter, offering significant discovery potential. At the same time, the complexity of the data and the presence of unknowable systematics pose significant challenges to robustly characterizing these signatures through conventional methods. I will describe how overcoming these challenges will require a qualitative shift in our approach to statistical inference in cosmology and astrophysics, bringing together several recent advances in probabilistic machine learning, differentiable programming, and simulation-based inference. I will showcase applications of these methods to astrophysical systems over a wide range of scales, from the motions of stars in our Galaxy to the distribution of large-scale structure, emphasizing how these analyses will drive significant progress on the dark matter question over the next decade.
