<p>The search for the conjectured QCD critical point in heavy-ion collisions requires to account for far-from equilibrium effects as well as fluctuations, and in particular non-Gaussian fluctuations, in the modeling of the dynamics of the hot and dense matter created in such collisions. In order to study far-from equilibrium effects as well as fluctuations, in this work we construct a Schwinger-Keldysh effective field theory (EFT) for the diffusion of the density to all orders in derivatives. The dissipation in the free part of our EFT follows the Boltzmann equation in the relaxation-time approximation (RTA). The interaction part of the EFT is constructed based on the self-interaction of the density field. We analytically find the quadratic and cubic parts of the KMS-invariant EFT in closed form, resummed in derivatives. We then explicitly compute the symmetrized three-point function at tree level, and investigate its analytical structure in detail. We also analytically calculate the branch-point singularity that appears in the structure of the two-point response function due to loop effects. Our results are important for future studies of the real-time dynamics of the correlation functions and the possible relation to thermalization when the system is far from equilibrium.</p>