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 $t^prime/t$.
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