# Sparse Data Diffusion for Scientific Simulations in Biology and Physics

arXiv: https://arxiv.org/abs/2502.02448 · HTML: https://mlsanity.com/paper/2502.02448/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Soft Weight-Sharing for Neural Network Compression](https://mlsanity.com/paper/1702.04008/) (2017)
- [Heavy-Tailed Diffusion Models](https://mlsanity.com/paper/2410.14171/) (2024)
- [UniGS: Unified Representation for Image Generation and Segmentation](https://mlsanity.com/paper/2312.01985/) (2023)
- [scDiffusion: conditional generation of high-quality single-cell data using diffusion model](https://mlsanity.com/paper/2401.03968/) (2024)
- [A Complete Recipe for Diffusion Generative Models](https://mlsanity.com/paper/2303.01748/) (2023)
- [Defect Spectrum: A Granular Look of Large-Scale Defect Datasets with Rich Semantics](https://mlsanity.com/paper/2310.17316/) (2023)
- [Poisson-Randomized Gamma Dynamical Systems](https://mlsanity.com/paper/1910.12991/) (2019)
- [Poisson--Gamma Dynamical Systems](https://mlsanity.com/paper/1701.05573/) (2017)
- [Deep Poisson gamma dynamical systems](https://mlsanity.com/paper/1810.11209/) (2018)

## Built on by (most cited first, 1 of 1)

- [Autoregressive Synthesis of Sparse and Semi-Structured Mixed-Type Data](https://mlsanity.com/paper/2603.01444/) (2026)

## Abstract (arXiv)

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.