Having isolated the velocity of the fluid seen as the key variable to include in the particle state vector, we need to devise a stochastic model to capture its dynamical evolution. The purpose of this chapter is therefore to explain the rationale behind its representation as a stochastic diffusion process and to introduce the state-of-the-art formulation. Following a bottom-up approach, we start with the analysis of the physics of particle dispersion in turbulent flows to work out how relevant timescales can be expressed. A second step consists in revisiting Kolmogorov theory to show that a stochastic diffusion model has physical support, though further approximations have to be made compared to the case of fluid particles. A stochastic model for the velocity of the fluid seen is then built by relying on present Langevin models for fluid particles, which are extended to accommodate the specific timescales of the velocity of the fluid seen. At the moment, such a construction respecting a set of well-established criteria has been achieved only for one model whose characteristics are worth presenting if we are to overcome this limitation with improved formulations in the following chapters.