Neutron diffraction is a versatile experimental technique capable of probing a material's magnetic properties. While diffraction is typically used to determine the magnetic structure of a material, magnetic diffuse scattering data from a diffraction experiment are also sensitive to the magnetic interactions in its Hamiltonian. However, accurately determining magnetic interaction parameters from neutron-scattering data involves an inverse scattering problem that is challenging to solve in general. Here, we investigate the effectiveness of a machine learning approach to predict the interaction parameters given magnetic diffuse-scattering data measured on powder samples, for a comprehensive survey of isotropic interactions on eight high-symmetry lattices. Across all lattices we considered, the machine-learning approach estimates the interaction parameters with high ( 2%) accuracy, while avoiding the issue of false minima that is encountered with non-linear least squares refinement. Our results highlight that powder diffuse-scattering data can provide a compact "fingerprint" of the magnetic interactions for many materials.