Mapping of source-hydrogenous medium systems within the framework of three-group diffusion theory is discussed. Each system is presented by the point of the map with coordinates: X ratio of first- and second-group diffusion lengths, and Г ratio of slowing down and thermal diffusion lengths. This mapping leads to the method of source-medium systems classification, which reduces the phase space of the problem. In accordance with this method, source-medium systems can be characterized by only two parameters, scale and shape. Thermal flux in the systems with the same shape parameter can be described with the same “generalized flux function (GFF).” The approach of GFFs is investigated for direct and inverse problems. The first one is presentation of thermal flux for certain source-medium systems with the help of these functions, and the second one is estimation of medium neutron transport parameters from the measured thermal flux through GFFs.