Walsh diagrams were first introduced by A.D. Walsh, a British chemistry professor at the University of Dundee, in a series of ten papers in one issue of the Journal of the Chemical Society.  Here, he aimed to rationalize the shapes adopted by polyatomic molecules in the ground state as well as in excited states, by applying theoretical contributions made by Mulliken.  Specifically, Walsh calculated and explained the effect of changes in the shape of a molecule on the energy of molecular orbitals.  Walsh diagrams are an illustration of such dependency, and his conclusions are what are referred to as the "rules of Walsh."
In his publications, Walsh showed through multiple examples that the geometry adopted by a molecule in its ground state primarily depends on the number of its valence electrons. He himself acknowledged that this general concept was not novel, but explained that the new data available to him allowed the previous generalizations to be expanded upon and honed.  He also noted that Mulliken had previously attempted to construct a correlation diagram for the possible orbitals of a polyatomic molecule in two different nuclear configurations, and had even tried to use this diagram to explain shapes and spectra of molecules in their ground and excited states.   However, Mulliken was unable to explain the reasons for the rises and falls of certain curves with increases in angle, thus Walsh claimed "his diagram was either empirical or based upon unpublished computations."