Since the model in which the water molecules form partially “ice-like” clusters explains the thermodynamic properties, the so-called itinerant oscillator model is applied to the motion of water molecules. The assumption is made that the atoms in a molecule receive stochastic forces from the neighboring molecules. The model of water with the stochastic force, of which the correlation functions are a delta function and a simple exponential, is discussed. The generalized frequency distributions of light and heavy water are derived from the model. The incoherent calculations of scattering laws of light and heavy water are compared with measurements. The model predicts well the total scattering cross section of light water, but the average cosine of scattering angle is slightly higher than that of the experiment. Further refinements in the model are discussed.