Stable diffeomorphism conjecture for torsion-free fundamental groups

Let $M$ and $N$ be closed, orientable, smooth $4$-manifolds that are homotopy equivalent and have torsion-free fundamental group. Stable diffeomorphism conjecture. Then $M$ and $N$ are stably diffeomorphic, meaning that for some non-negative integers $r$ and $s$, $M\# r(S^2\times S^2)$ is diffeomorphic to $N\# s(S^2\times S^2)$. This is known in the simply connected case and for many classes of fundamental groups, but is not established for all torsion-free groups.