Clarifying the structure/dynamics relation of water hydrogen-bond network has been the aim of extensive research over many decades. By joining anvil cell high-pressure technology, femtosecond 2D infrared spectroscopy, and molecular dynamics simulations, we studied, for the first time, the spectral diffusion of the stretching frequency of an HOD impurity in liquid water as a function of pressure. Our experimental and simulation results concordantly demonstrate that the rate of spectral diffusion is almost insensitive to the applied pressure. This behavior is in contrast with the previously reported pressure-induced speed up of the orientational dynamics, which can be rationalized in terms of large angular jumps involving sudden switching between two hydrogen-bonded configurations. The different trend of the spectral diffusion can be, instead, inferred considering that the first solvation shell preserves the tetrahedral structure with pressure and the OD stretching frequency is only slight perturbed.