Diffusion models (DMs) excel on dense continuous data, but are not designed for sparse continuous data. They do not model exact zeros that represent the deliberate absence of a signal. As a result, they erase sparsity patterns and perform unnecessary computation on mostly zero entries. With Sparsity-Exploiting Diffusion (SED), we model only non-zero values, preserving sparsity. SED delivers computational savings while maintaining or improving generation quality by skipping zeros during training and inference. Across physics and biology benchmarks, SED matches or surpasses conventional DMs and domain-specific baselines, while vision experiments provide intuitive insights into the limitations of dense DMs and the benefits of SED.
@article{arxiv.2605.01817,
title = {Skipping the Zeros in Diffusion Models for Sparse Data Generation},
author = {Phil Sidney Ostheimer and Mayank Nagda and Andriy Balinskyy and Gabriel Vicente Rodrigues and Jean Radig and Carl Herrmann and Stephan Mandt and Marius Kloft and Sophie Fellenz},
journal= {arXiv preprint arXiv:2605.01817},
year = {2026}
}