The origin of the diffuse interstellar bands (DIBs), one of the longest-standing mysteries of the interstellar medium (ISM), is explored within the framework of The Heterogeneous dust Evolution Model for Interstellar Solids (THEMIS). The likely nature of the DIB carriers and their evolution is here explored within the framework of the structures and sub-structures inherent to doped hydrogenated amorphous carbon grains in the ISM. Based on the natural aromatic-rich moieties (asphaltenes) recovered from coal and oil, the likely structure of their interstellar analogues is investigated within the context of the diffuse band problem. It is here proposed that the top-down evolution of interstellar carbonaceous grains, and, in particular, a-C(:H) nanoparticles, is at the heart of the formation and evolution of the DIB carriers and their associations with small molecules and radicals, such as C2, C3, CH and CN. It is most probable that the DIBs are carried by dehydrogenated, ionized, hetero-cyclic, olefinic and aromatic-rich moieties that form an integral part of the contiguous structure of hetero-atom-doped hydrogenated amorphous carbon nanoparticles and their daughter fragmentation products. Within this framework, it is proposed that polyene structures in all their variants could be viable DIB carrier candidates.