  We study the 2d directed polymer in random environment in a novel
*quasi-critical regime*, which interpolates between the much studied
sub-critical and critical regimes. We prove Edwards-Wilkinson fluctuations
throughout the quasi-critical regime, showing that the diffusively rescaled
partition functions are asymptotically Gaussian, under a rescaling which
diverges arbitrarily slowly as criticality is approached. A key challenge is
the lack of hypercontractivity, which we overcome deriving new sharp moment
estimates.
