The pump-probe response of water in infrared is examined theoretically at time scales of the order of 100 fs; these times scales are characteristic of spectral diffusion. The theory is a statistical theory using correlation function description of the nonlinear optical processes involved. An analytical expression for the transient infrared signal is presented, and the corresponding time- and frequency-resolved spectra are discussed. Real time shifts of spectral bands, preceded by a redistribution of their intensities, are predicted. Physical interpretation of these findings is proposed, corroborated by the help of simple models. The intrinsic interest of this time domain is emphasized.