We consider a class of conditional McKean-Vlasov processes that arise in the study of interacting Langevin diffusions on regular trees. We establish an H-theorem that characterizes the long-time behavior of these processes. Specifically, we show that a certain function that arises when taking the limit of certain renormalized relative entropies serves as a global Lyapunov function for the associated measure flow. We also provide counterexamples to highlight some subtleties in the approach, and discuss some open problems. This is joint work with Kevin Hu.