Molecules are ubiquitous in space. They are necessary components in the creation of habitable planetary systems and can provide the basic building blocks of life. Solid-state processes are pivotal in the formation of molecules in space and surface diffusion in particular is a key driver of chemistry in extraterrestrial environments, such as the massive clouds in which stars and planets are formed and the icy objects within our solar system. However, for many atoms and molecules quantitative theoretical and experimental information on diffusion, such as activation barriers, are lacking. This hinders us in unravelling chemical processes in space and determining how the chemical ingredients of planets and life are formed. In this article, an astrochemical perspective on diffusion is provided. Described are the relevant adsorbate-surface systems, the methods to model their chemical processes, and the computational and laboratory techniques to determine diffusion parameters, including the latest developments in the field. While much progress has been made, many astrochemically relevant systems remain unexplored. The complexity of ice surfaces, their temperature-dependent restructuring, and effects at low temperatures create unique challenges that demand innovative experimental approaches and theoretical frameworks. This intersection of astrochemistry and surface science offers fertile ground for physical chemists to apply their expertise. We invite the physical chemistry community to explore these systems, where precise diffusion parameters would dramatically advance our understanding of molecular evolution in space—from interstellar clouds to planetary surfaces—with implications on our understanding on the origins of life and planetary habitability.