How to add correlated noise to a mathematical model of observed data?

I got the same error, and after commenting it out deep in the Pymc source code, there started appearing divergences when running NUTS. It could be the case that NUTS, unlike SMC-ABC is fundamentally unable to include such random correlated noise. Could someone confirm?
It would be a shame because adding correlated noise is important in two cases: when observed data has correlated uncertainties and when some of the mathematical model’s input parameters are not designated to have their priors updated. SMC-ABC works but is much more computationally heavy than NUTS.