I have N data points which are most easily modeled as a multivariate normal distribution, with the mean/covariance dependent on the parameters of the model \theta i.e.

y \sim \mathcal{N}(\mu (x;\theta),\Sigma(\theta))

My question is, is there a way to cross-validate this model effectively? I see that the Vehtari, Gelman, and Gabry paper on loo makes the assumption that the data are independent conditional on the parameters. Are there alternatives that would work for this case?