Invertibility conjecture for the hyperkähler Nahm transform

Let $M$ and $N$ be two connected 4-dimensional hyperkähler manifolds. Suppose that $N$ is a connected component of the moduli space of instantons on $M$, and $M$ is a connected component of the moduli space of instantons on $N$.

Hyperkähler Nahm transform conjecture. Then $M$ is diffeomorphic to $N$, and the hyperkähler Nahm transform is invertible.

This conjecture proposes that mutually realized instanton moduli spaces are diffeomorphic and that the corresponding Nahm transforms are inverse to one another. The supplied text gives no resolution, so the conjecture remains open.