Sparse Data Diffusion for Scientific Simulations in Biology and Physics

Phil Ostheimer, Mayank Nagda, Andriy Balinskyy, Jean Radig, Carl Herrmann, Stephan Mandt, Marius Kloft, Sophie Fellenz

Keywords: sparse generative modeling in biology and physics, diffusion models, data sparsity

TL;DR: Sparse Data Diffusion is a diffusion-based simulator that adds Sparsity Bits to explicitly model exact zeros, yielding higher-fidelity sparse simulations in particle physics and single-cell biology than common baselines.

Abstract: Sparse data is fundamental to scientific simulations in biology and physics, from single-cell gene expression to particle calorimetry, where exact zeros encode physical absence rather than weak signal. However, existing diffusion models lack the physical rigor to faithfully represent this sparsity. This work introduces Sparse Data Diffusion (SDD), a generative method that explicitly models exact zeros via Sparsity Bits, unifying efficient ML generation with physically grounded sparsity handling. Empirical validation in particle physics and single-cell biology demonstrates that SDD achieves higher fidelity than baseline methods in capturing sparse patterns critical for scientific analysis, advancing scalable and physically faithful simulation.

Release To Public: Yes, please release this paper to the public

Submission Number: 13