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We present our work on end-to-end training of acoustic models using the lattice-free maximum mutual information (LF-MMI) objective function in the context of hidden Markov models. By end-to-end training, we mean flat-start training of a single DNN in one stage without using any previously trained models, forced alignments, or building state-tying decision trees. We use full biphones to enable context-dependent modeling without trees and show that our end-to-end LF-MMI approach can achieve comparable results to regular LF-MMI on well-known large vocabulary tasks. We also compare with other end-to-end methods such as CTC in character-based and lexicon-free settings and show 5 to 25 percent relative reduction in word error rates on different large vocabulary tasks while using significantly smaller models.