  The field of language modelling has been largely dominated by autoregressive
models, for which sampling is inherently difficult to parallelize. This paper
introduces two new classes of generative models for categorical data such as
language or image segmentation: Argmax Flows and Multinomial Diffusion. Argmax
Flows are defined by a composition of a continuous distribution (such as a
normalizing flow), and an argmax function. To optimize this model, we learn a
probabilistic inverse for the argmax that lifts the categorical data to a
continuous space. Multinomial Diffusion gradually adds categorical noise in a
diffusion process, for which the generative denoising process is learned. We
demonstrate that our models perform competitively on language modelling and
modelling of image segmentation maps.
