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This paper gives a spectral algorithm for learning HMM from non-sequential observations. Motivated by several scientific examples, the authors define a sampling model for non-sequential observations that shares some similarities with the generative model of Latent Dirichlet Allocation. Then, resorting to recent spectral techniques for learning LDA, HMM, and mixture models, they prove sample bounds for recovering the parameters of an HMM with continuous output from data sampled according to this model. The last section provides a simple simulation that illustrates the behavior of the algorithm in a synthetic example. Proofs of all results are given in the supplementary material.