When sampling measures on Hilbert spaces one option is to first discretize the space and then apply standard Markov Chain Monte Carlo methods. This works but the finer the discretization is, the slower convergence rate of the chains is. Alternatively one can also first consider a well defined method on the function space directly and afterwards discretize. I will talk about a version of the HMC method on Hilbert spaces that has a diffusion limit converging to an SPDE. This leads to methods that converge equally well independently of the chosen discretization.