Jumping up and down: Denoiser diffusion models for discrete ordinal data

2026-10-01

AI Summary

This study addresses the challenge that existing diffusion models struggle to effectively handle discrete ordinal data, such as images, music, and gene counts. To this end, we propose the JUD model family, introducing the first denoiser-based diffusion framework tailored for ordinal data. This framework incorporates a bidirectional perturbation mechanism that supports both upward and downward state transitions, thereby simplifying the training objective while substantially enhancing modeling flexibility. Experimental results demonstrate that JUD achieves highly competitive performance across generative tasks involving multiple data modalities, validating the effectiveness and versatility of the proposed approach in modeling discrete ordinal data.

Abstract

Diffusion models are highly developed in continuous spaces for image and video domains. Recently, major advances have been made for discrete diffusion models for categorical data, specifically in the language domain. In contrast, diffusion models for discrete integer-valued data are less developed, despite the prevalence of this modality, ranging from images and music to gene counts. We introduce Jumping Up and Down (JUD)---a new family of denoiser-based diffusion models for discrete ordinal data. This is the first family of diffusion models for ordinal data which centers around training denoisers, which at the same time allows for bi-directional (up and down) perturbations of the data. The simplicity of the training objective, combined with the flexibility of bi-directional perturbations, leads us to obtain competitive results across different data modalities.

Problem

• diffusion models
• discrete ordinal data
• denoiser
• integer-valued data

Innovation

• Diffusion Models
• Discrete Ordinal Data
• Denoiser
• Bidirectional Perturbation
• JUD