in the script specifying_mass_matrices.py dense mass matrices are used and their structure can be investigated in wa_state.mass_matrix_sqrt or wa_init
the most general form (and also that which should be straightforward from the MV-normal built by SVI) should be the complete mass matrix, provided as a dictionary of a tuple of all $n$ parameter names and the corresponding $n \times n$ matrix as a value.
Elements, which should be considered independent, i.e. not correlated to any other variables, could be specified only in terms of their standard deviation (in the diagonal of the matrix)
[ ] Ask in numypro forum if this would technically work.
specifying_mass_matrices.pydense mass matrices are used and their structure can be investigated inwa_state.mass_matrix_sqrtorwa_initnumyproforum if this would technically work.