  Denoising diffusion probabilistic models (DDPMs) have shown impressive
results on sequence generation by iteratively corrupting each example and then
learning to map corrupted versions back to the original. However, previous work
has largely focused on in-place corruption, adding noise to each pixel or token
individually while keeping their locations the same. In this work, we consider
a broader class of corruption processes and denoising models over sequence data
that can insert and delete elements, while still being efficient to train and
sample from. We demonstrate that these models outperform standard in-place
models on an arithmetic sequence task, and that when trained on the text8
dataset they can be used to fix spelling errors without any fine-tuning.
