The holographic RG of Anti-De Sitter gives a powerful clue about the underlying AdS/CFT correspondence. The question is whether similar hints can be found for the heretofore elusive holographic dual of De Sitter. The framework of stochastic inflation uses a nonperturbative insight in order to tame bad behavior in the perturbation series at late times. Recasting this as a "resummation of time", we wish understand whether the distributions that result can be thought of as an attractive UV fixed point of a theory living on a spacelike slice of DS. I will discuss our rederivation of stochastic inflation in terms of wavefunctionals, the straightforward way one can implement corrections to the leading approximations, and the robustness of the late-time equilibrium to perturbations.