Scalar gaussian noise for a multivariate model

We let the user to choose between a "gaussian-diagonal" and a "gaussian-scalar" observational model when implementing a multivariate model. The difference between the two methods is that the "diagonal" option adds a noise for each feature (1<=k<=d) corresponding to :

while the "scalar" adds a global noise shared between all the features, corresponding to :

My question is, do we really need to keep the scalar option for a multivariate model? I thought that the basic formulation for the DCM uses the diagonal noise.