Abstract: We consider unsupervised estimation of mixtures of discrete graphical models, where the class variable is hidden and each mixture component can have a potentially different Markov graph structure and parameters over the observed variables. We propose a novel method for estimating the mixture components with provable guarantees. Our output is a tree-mixture model which serves as a good approximation to the underlying graphical model mixture. The sample and computational requirements for our method scale as $\poly(p, r)$, for an $r$-component mixture of $p$-variate graphical models, for a wide class of models which includes tree mixtures and mixtures over bounded degree graphs.