  The diffusion model has been a crucial component in studies about social
networks. Many studies, especially these about influence maximization concern
the proof of the submodularity of particular diffusion models. Such proofs have
been model-dependent and are somewhat ad hoc. In this paper, we prove a theorem
that provides a necessary and sufficient condition for a diffusion model to be
submodular. This theorem can be used to justify the submodularity of an
arbitrary diffusion model. We also apply this theorem to build a projection
operator that maps an arbitrary diffusion model into a submodular one.
Moreover, we use the established theorem to propose a diffusion model of
multiple heterogeneous pieces of information that partially features
submodularity.
