Weak coupling limit of KPZ with rougher than white noise

We consider the KPZ equation in 1 spatial dimension with noise that is rougher than white by an exponent >1/4. Under a weak coupling limit, formally removing the nonlinearity from the equation, we show using regularity structures that the renormalised solutions converge to a Gaussian limit that is different from the solution of the linear part of the equation. The regime of this effect has a nontrivial overlap with the subcritical regime <1/2.