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Learning a categorical distribution comes with its own set of challenges. Asuccessful approach taken by state-of-the-art works is to cast the problem in acontinuous domain to take advantage of the impressive performance of thegenerative models for continuous data. Amongst them are the recently emergingdiffusion probabilistic models, which have the observed advantage of generatinghigh-quality samples. Recent advances for categorical generative models havefocused on log likelihood improvements. In this work, we propose a generativemodel for categorical data based on diffusion models with a focus onhigh-quality sample generation, and propose sampled-based evaluation methods.The efficacy of our method stems from performing diffusion in the continuousdomain while having its parameterization informed by the structure of thecategorical nature of the target distribution. Our method of evaluationhighlights the capabilities and limitations of different generative models forgenerating categorical data, and includes experiments on synthetic andreal-world protein datasets.

Diffusing Gaussian Mixtures for Generating Categorical Data