Without knowing details of your model it’s hard to say more, but sometime models that are SPD in exact arithmetic fail to have a Cholesky decomposition in floating point arithmetic.
It’s possible that adding 1e-12 is not enough. You can look at the detailed forwards error analysis of a cholesky decomposition (which will tell you you need to consider the condition number of Sigma), or you can do what the rest of us do and replace 1e-12 (which is far to small with either 1e-7 or 1e-5.