  Non-autoregressive models greatly improve decoding speed over typical
sequence-to-sequence models, but suffer from degraded performance. Infilling
and iterative refinement models make up some of this gap by editing the outputs
of a non-autoregressive model, but are constrained in the edits that they can
make. We propose iterative realignment, where refinements occur over latent
alignments rather than output sequence space. We demonstrate this in speech
recognition with Align-Refine, an end-to-end Transformer-based model which
refines connectionist temporal classification (CTC) alignments to allow
length-changing insertions and deletions. Align-Refine outperforms Imputer and
Mask-CTC, matching an autoregressive baseline on WSJ at 1/14th the real-time
factor and attaining a LibriSpeech test-other WER of 9.0% without an LM. Our
model is strong even in one iteration with a shallower decoder.
