Recently, End-to-End (E2E) frameworks have achieved remarkable results on\nvarious Automatic Speech Recognition (ASR) tasks. However, Lattice-Free Maximum\nMutual Information (LF-MMI), as one of the discriminative training criteria\nthat show superior performance in hybrid ASR systems, is rarely adopted in E2E\nASR frameworks. In this work, we propose a novel approach to integrate LF-MMI\ncriterion into E2E ASR frameworks in both training and decoding stages. The\nproposed approach shows its effectiveness on two of the most widely used E2E\nframeworks including Attention-Based Encoder-Decoders (AEDs) and Neural\nTransducers (NTs). Experiments suggest that the introduction of the LF-MMI\ncriterion consistently leads to significant performance improvements on various\ndatasets and different E2E ASR frameworks. The best of our models achieves\ncompetitive CER of 4.1\\% / 4.4\\% on Aishell-1 dev/test set; we also achieve\nsignificant error reduction on Aishell-2 and Librispeech datasets over strong\nbaselines.\n