We use argon step-release measurements to model the initial distribution of argon isotopes in 177 lunar impact spherules. The speed of modern computers permits us to approach this inverse problem in new ways, and the techniques we develop may be extended to study a wide range of samples, diffusing species, and geometries. Lunar spherules, by virtue of their simple shapes and histories, seem to be excellent candidates for inverse modeling. Nevertheless, impact spherules preserve chemical or material heterogeneities that are relics of their parent materials. As a result, we find that the distribution of argon isotopes in most impact spherules is more complex than can be meaningfully constrained by a practical number of precise measurements. The spatial distribution of argon from different sources, such as solar implantation, would be better probed in spherules by other techniques, such as stepwise etching.