Among the questions that would be raised by the observation of a new resonance at the LHC, particularly pressing are those concerning the production mechanism: What is the initial state? Is the resonance produced independently or in association with other particles? Here we present two weakly-coupled renormalizable models for production of a diphoton resonance that differ in both their initial and final states. In one model, a scalar particle produced through gluon fusion decays into a diphoton particle and a light, long-lived pseudoscalar. In another model, a boson produced from the annihilation of a strange-antistrange quark pair undergoes a cascade decay that leads to a diphoton particle and two sterile neutrinos. Various kinematic distributions may differentiate these models from the canonical model where a diphoton particle is directly produced in gluon fusion.