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In the last years, a few experiments in the fields of biological and soft matter physics in colloidal suspensions have reported normal diffusion with a Laplacian probability distribution in the particles displacements (i.e., Brownian yet non Gaussian diffusion). To model this behavior different stochastic models had been proposed, with all of them introducing new random elements that incorporate our lack of information about the media. Although these models work in practice, due to their own nature a thorough understanding of how the media interacts with itself and with the Brownian particle in Brownian yet non Gaussian diffusion is outside of their aim and scope. For this reason, a comprehensive mathematical model to explain Brownian yet non Gaussian diffusion that includes molecular interactions is proposed in this paper. Based on the theory of interfaces by Gennes and Langevin dynamics, it is shown that long-range interactions in a weakly interacting fluid and in a microscopic regime of zero viscosity leads to a Laplacian probability distribution in the particles displacements. Further, it is shown that a phase transition can explain a high diffusivity and causes this Laplacian distribution to evolve towards a Gaussian via a transition probability in the interval of time as it was observed in experiments. To validate these model predictions, the experimental data of the Brownian motion of colloidal beads on phospholipid bilayer by Wang et al. is used and compared with the results of the theory. This comparison suggests that the proposed model not only is able to explain qualitatively the Brownian yet non-Gaussian diffusion, but also quantitatively.