Skipping the Zeros in Diffusion Models for Sparse Data Generation

Phil Sidney Ostheimer; Mayank Nagda; Andriy Balinskyy; Gabriel Vicente Rodrigues; Jean Radig; Carl Herrmann; Stephan Mandt; Marius Kloft; Sophie Fellenz

arXiv · 2605.01817

Skipping the Zeros in Diffusion Models for Sparse Data Generation

Phil Sidney Ostheimer·Mayank Nagda·Andriy Balinskyy·Gabriel Vicente Rodrigues·Jean Radig·Carl Herrmann·Stephan Mandt·Marius Kloft·Sophie Fellenz

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Abstract

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.

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Phil Sidney Ostheimer, Mayank Nagda, Andriy Balinskyy, Gabriel Vicente Rodrigues, Jean Radig, Carl Herrmann, Stephan Mandt, Marius Kloft, Sophie Fellenz. 2026-05-03. Skipping the Zeros in Diffusion Models for Sparse Data Generation. https://arxiv.org/abs/2605.01817

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