Transformer-based autoregressive (AR) machine translation models have achieved significant performance improvements, nearing human-level accuracy on some languages. The AR framework translates one token at a time which can be time consuming, especially for long sequences. To accelerate inference, recent work has been exploring non-autoregressive (NAR) approaches that translate blocks of tokens in parallel. Despite significant progress, leading NAR models still lag behind their AR counterparts, and only become competitive when trained with distillation. In this paper we investigate possible reasons behind this performance gap, namely, the indistinguishability of tokens, and mismatch between training and inference. We then propose the Conditional Masked Language Model with Correction (CMLMC) that addresses these problems. Empirically, we show that CMLMC achieves state-of-the-art NAR performance when trained on raw data without distillation and approaches AR performance on multiple datasets. Full code for this work will be released at the time of publication.