  Much effort has been spent in recent years on restoring uniqueness of
McKean-Vlasov SDEs with non-smooth coefficients. As a typical instance, the
velocity field is assumed to be bounded and measurable in its space variable
and Lipschitz-continuous with respect to the distance in total variation in its
measure variable, see [Jourdain, Mishura-Veretennikov]. In contrast with those
works, we consider in this paper a Fokker-Planck equation driven by an
infinite-dimensional noise, inspired by the diffusion models on the Wasserstein
space studied in [Konarovskyi, Marx]. We prove that well-posedness of that
equation holds for a drift function that might be only bounded and measurable
in its measure argument, provided that a trade-off is respected between the
regularity in the finite-dimensional component and the regularity in the
measure argument. In this regard, we show that the higher the regularity of b
with respect to its space variable is, the lower regularity we have to assume
on b with respect to its measure variable in order to restore uniqueness.
