# Fast 3D Diffusion for Scalable Granular Media Synthesis

arXiv: https://arxiv.org/abs/2508.19752 · HTML: https://mlsanity.com/paper/2508.19752/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 27 Aug 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2304.08818/) (2023)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Generative Diffusion Models on Graphs: Methods and Applications](https://mlsanity.com/paper/2302.02591/) (2023)
- [GraphGen: A Scalable Approach to Domain-agnostic Labeled Graph Generation](https://mlsanity.com/paper/2001.08184/) (2020)
- [Diffusion Models, Image Super-Resolution And Everything: A Survey](https://mlsanity.com/paper/2401.00736/) (2024)
- [Tutorial on Diffusion Models for Imaging and Vision](https://mlsanity.com/paper/2403.18103/) (2024)

## Abstract (arXiv)

Discrete Element Method (DEM) simulations of granular media are computationally intensive, particularly during initialization phases dominated by large displacements and kinetic energy. This paper presents a novel generative pipeline based on 3D diffusion models that directly synthesizes arbitrarily large granular assemblies in mechanically realistic configurations. The approach employs a two-stage pipeline. First, an unconditional diffusion model generates independent 3D voxel grids representing granular media; second, a 3D inpainting model, adapted from 2D techniques using masked inputs and repainting strategies, seamlessly stitches these grids together. The inpainting model uses the outputs of the unconditional diffusion model to learn from the context of adjacent generations and creates new regions that blend smoothly into the context region. Both models are trained on binarized 3D occupancy grids derived from a database of small-scale DEM simulations, scaling linearly with the number of output voxels. Simulations that spanned over days can now run in hours, practically enabling simulations containing more than 200k ballast particles. The pipeline remains fully compatible with existing DEM workflows as it post-processes the diffusion generated voxel grids into DEM compatible particle meshes. Being mechanically consistent on key granulometry metrics with the original DEM simulations, the pipeline is also compatible with many other applications in the field of granular media, with capability of generating both convex and non-convex particles. Showcased on two examples (railway ballast and lunar regolith), the pipeline reimagines the way initialization of granular media simulations is performed, enabling scales of generation previously unattainable with traditional DEM simulations.