Abstract: We will show how to associate to the data of a noncommutative geometry an open quantum system which carries a natural quantum diffusion process. We will consider how this process generalizes the classical Laplacian generated diffusion. We will introduce needed ideas from noncommutative probability, and consider quantum analogs of the Feynman-Kac formulae which we apply to evaluating the spectral action. Finally we highlight some unexplored possibilities which are opened by this mixing of noncommutative probability and geometry.