To rationalize the fact that lifetimes of the diffuse states appear in the emission of the sharp states, the FWM pathways participating in this experiment can be considered with diagrammatic perturbation theory, a method used to depict the evolution of a quantum system in response to multiple pulse interactions . A nonlinear process, FWM emission arises from the third-order polarization of the medium and is therefore described by three, perturbative light-matter interactions. As shown in Fig. , a resonant FWM pathway can be initiated by an XUV photon that excites CO2 from its ground state to either a Henning diffuse or Henning sharp state. Two NIR photons then couple the XUV-excited Rydberg state to itself or other states within the NIR bandwidth via a resonant dark state, generating a third order polarization response that results in the emission of a photon with the energy of the final state. As a result, four different types of pathways depending on the initial excitation and final emission states can be enumerated: diffuseto-sharp pathways (Fig. ), diffuse-to-diffuse pathways (Fig. ), sharp-to-sharp pathways (Fig. ), and sharp-to-diffuse pathways (Fig. ). For transient measurements in which the two NIR pulses are delayed with respect to the XUV pulse, the dynamics measured will encode the lifetime of the state initially excited by the XUV photon, rather than the state from which the photon emits .