The two-dimensional KPZ equation in the entire subcritical regime

We consider the KPZ equation in space dimension 2 driven by space-time white noise. We showed in previous work that if the noise is mollified in space on scale . and its strength is scaled as .^/|log.|......, then a transition occurs with explicit critical point .^c=2..... Recently Chatterjee and Dunlap showed that the solution admits subsequential scaling limits as ..0, for sufficiently small .^. We prove here that the limit exists in the entire subcritical regime .^.(0,.^c) and we identify it as the solution of an additive stochastic heat equation, establishing so-called Edwards.Wilkinson fluctuations. The same result holds for the directed polymer model in random environment in space dimension 2.