Upcoming astronomical surveys like Euclid and LSST will probe the matter distribution down to scales of less than 1 Mpc/h with percent-level precision. Confronting these observations with theoretical predictions, though, will be challenging for at least two reasons: On the one hand, these scales lie far within the nonlinear regime of structure formation where conventional Eulerian and Lagrangian analytic approaches break down. On the other hand, baryonic effects like gas dynamics and astrophysical feedback become relevant on these small scales. In this talk I will describe an analytic framework that aims at overcoming both of these challenges. It is built on the Kinetic Field Theory approach developed by Bartelmann et al. and extends it to the treatment of a gravitationally coupled system of dark and baryonic matter. I will first present nonlinear results of the structure formation in pure dark matter and compare these to the results found in standard Eulerian perturbation theory. After that I will describe how baryonic gas dynamics can be taken into account and show linear results on the small-scale structure formation in coupled dark and baryonic matter. I will conclude with an outlook on the planned further developments of this framework.