# Controlled Latent Diffusion Models for 3D Porous Media Reconstruction

arXiv: https://arxiv.org/abs/2503.24083 · HTML: https://mlsanity.com/paper/2503.24083/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 31 Mar 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, 12 of 12)

- [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)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Heavy-Tailed Diffusion Models](https://mlsanity.com/paper/2410.14171/) (2024)
- [Reconstruction of three-dimensional porous media using generative adversarial neural networks](https://mlsanity.com/paper/1704.03225/) (2017)
- [Lettuce: PyTorch-based Lattice Boltzmann Framework](https://mlsanity.com/paper/2106.12929/) (2021)
- [Latent diffusion models for parameterization and data assimilation of facies-based geomodels](https://mlsanity.com/paper/2406.14815/) (2024)

## Built on by (most cited first, 5 of 5)

- [The Effect of Stochasticity in Score-Based Diffusion Sampling: a KL Divergence Analysis](https://mlsanity.com/paper/2506.11378/) (2025)
- [Synergizing Transport-Based Generative Models and Latent Geometry for Stochastic Closure Modeling](https://mlsanity.com/paper/2602.17089/) (2026)
- [PCP-GAN: Property-Constrained Pore-scale image reconstruction via conditional Generative Adversarial Networks](https://mlsanity.com/paper/2510.19465/) (2025)
- [PoreDiT: A Scalable Generative Model for Large-Scale Digital Rock Reconstruction](https://mlsanity.com/paper/2604.10171/) (2026)
- [Physics-Guided Generative AI for Property-Targeted 3D Porous Media Design](https://mlsanity.com/paper/2607.24274/) (2026)

## Abstract (arXiv)

Note: The final version of this article was published in Computers and Geosciences, Volume 206, January 2026, 106038. DOI: 10.1016/j.cageo.2025.106038. Readers should refer to the published version for the most up-to-date content. Three-dimensional digital reconstruction of porous media presents a fundamental challenge in geoscience, requiring simultaneous resolution of fine-scale pore structures while capturing representative elementary volumes. We introduce a computational framework that addresses this challenge through latent diffusion models operating within the EDM framework. Our approach reduces dimensionality via a custom variational autoencoder trained in binary geological volumes, improving efficiency and also enabling the generation of larger volumes than previously possible with diffusion models. A key innovation is our controlled unconditional sampling methodology, which enhances distribution coverage by first sampling target statistics from their empirical distributions, then generating samples conditioned on these values. Extensive testing on four distinct rock types demonstrates that conditioning on porosity - a readily computable statistic - is sufficient to ensure a consistent representation of multiple complex properties, including permeability, two-point correlation functions, and pore size distributions. The framework achieves better generation quality than pixel-space diffusion while enabling significantly larger volume reconstruction (256-cube voxels) with substantially reduced computational requirements, establishing a new state-of-the-art for digital rock physics applications.