Good base for NLL for SDEs in latent space. Basically the 'chuck a diag gaussian head' of SDEs.
Think of the OU process as a river with a current. The current always tries to pull you toward the mean. A path is likely if it mostly cooperates with this current, and unlikely if it constantly fights against it.
If you need to predict complex SDEs that cannot be simply approximated with a gaussian processes, consider doing a normalising flow to transform it into dataspace from the OU base distribution.