Abstract: We study the problem of learning Censored Markov Random Fields (abbreviated CMRFs), which are Markov Random Fields where some of the nodes are censored (i.e. not observed). We assume the CMRF is high temperature but, crucially, make no assumption about its structure. This makes structure learning impossible. Nevertheless we introduce a new definition, which we call learning to sample, that circumvents this obstacle. We give an algorithm that can learn to sample from a distribution within $\epsilon n$ earthmover distance of the target distribution for any $\epsilon > 0$. We obtain stronger results when we additionally assume high girth, as well as computational lower bounds showing that these are essentially optimal.