  We introduce an efficient way to improve the accuracy of projected wave
functions, widely used to study the two-dimensional Hubbard model. Taking the
clue from the backflow contribution, whose relevance has been emphasized for
various interacting systems on the continuum, we consider many-body
correlations to construct a suitable approximation for the ground state at
intermediate and strong couplings. In particular, we study the phase diagram of
the frustrated $t{-}t^\prime$ Hubbard model on the square lattice and show
that, thanks to backflow correlations, an insulating and non-magnetic phase can
be stabilized at strong coupling and sufficiently large frustrating ratio
$t^\prime/t$.
