Right and this arguably is especially the case for high dimensional image datasets. Yet despite this case, we are able to train models on these high dimensional

Right and this arguably is especially the case for high dimensional image datasets. Yet despite this case, we are able to train models on these high dimensional dataset through MCMC (with some tricks) with good likelihood, indicating that standard MCMC technique can actually scale up to very high dimensional multi-modal situations which was previously thought to be computationally intractable.