We consider statistical models in which functional data are artificially contaminated by independent Wiener processes in order to satisfy privacy constraints. We show that the corrupted observations have a Wiener density, which determines the distribution of the original functional data uniquely. A nonparametric estimator of the functional density is constructed and its asymptotic properties are studied. We discuss real data applications in the fields of classification and goodness-of-fit testing. This talk is based on a joint work with Aurore Delaigle (University of Melbourne).