That won’t work unfortunately. We also need to draw MVN samples with the inverse of the mass matrix, and that seems tricky with that form. If you write it as D(VSV^T + I - VV^T)D that gets easy, because you can just invert D and S.
I don’t think it is that costly to make sure the columns are orthogonal. Finding the eigenvalues is pretty fast, even for large systems, and we only need to do it a couple of times.
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