Binomial flows: Denoising and flow matching for discrete ordinal data
It provides a principled connection between denoising and score functions for discrete ordinal data, addressing a gap in discrete flow-based generative modeling.
This work introduces Binomial flows, a framework for discrete ordinal data that unifies denoising, sampling, and likelihood estimation, achieving competitive results on real-world datasets.
Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, this relation has been largely missing in the discrete setting where common approaches focus on learning discrete scores and rates. In this work we close this gap for discrete non-negative ordinal data by introducing Binomial flows. Our framework provides a simple recipe for training a discrete diffusion model which simultaneously denoises, samples, and estimates exact likelihoods. We verify our methodology on synthetic examples and obtain competitive results on real-world data sets.