We consider a class of infinite-dimensional parabolic evolution equations driven by multiplicative rough stochastic noise. As main example we introduce a Brownian motion. In order to solve these equations in a mild pathwise sense we give a short introduction on rough paths theory. In particular we show how to lift a Brownian motion to a rough path. Then, by combining techniques from M. Gubinelli and S. Tindel (2010) together with arguments employed by M. Garrido, K. Lu and B. Schmalfuß (2015) we are able to define a rough integral and derive the existence of global solutions.This talk is based on a joint work with Alexandra Neamţu (TU Munich).