Theoretical descriptions of the time-resolved infrared-infrared visible (IIV) sum and difference frequency generation are presented. The IIV sum-frequency generation (SFG) method is shown to be useful in selectively studying the vibrational relaxation of the overtone mode. The IIV difference-frequency generation (DFG), which is a specific case of the doubly resonant four-wave mixing spectroscopies, involves a rephasing period so that the elimination of the vibrational inhomogeneous broadening can be achieved by using this method. The decay of the diagonal IIV-DFG signal is proven to be independent on the inhomogeneous distribution of the vibrational frequency. Furthermore, it is shown that the two-dimensional time-resolved IIV-DFG signal along the antidiagonal provides a direct information on the vibrational inhomogeneous distribution function.