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With recent advances in speech synthesis, synthetic data is becoming a viable alternative to real data for training speech recognition models. However, machine learning with synthetic data is not trivial due to the gap between the synthetic and the real data distributions. Synthetic datasets may contain artifacts that do not exist in real data such as structured noise, content errors, or unrealistic speaking styles. Moreover, the synthesis process may introduce a bias due to uneven sampling of the data manifold. We propose two novel techniques during training to mitigate the problems due to the distribution gap: (i) a rejection sampling algorithm and (ii) using separate batch normalization statistics for the real and the synthetic samples. We show that these methods significantly improve the training of speech recognition models using synthetic data. We evaluate the proposed approach on keyword detection and Automatic …