Advancements in machine learning have enabled new ways of performing inference on forward models defined through complex, high-dimensional simulations. After briefly motivating their use in the astrophysical context, I will present applications of these simulation-based inference (SBI) methods to two systems where the goal is to look for signatures of dark matter that are connected to its underlying particle physics properties. First, I will describe how SBI techniques can be used to combine information from thousands of strong gravitational lensing systems in a principled way to extract the population properties of dark matter subhalos. Then, I will show how SBI methods can probe the collective effect of dark matter subhalos in the Milky Way on the measured motions of background celestial objects imprinted through astrometric lensing. In concluding, I will emphasize the wide applicability of machine learning-accelerated SBI methods for new physics searches through further examples.