# Latent diffusion models for parameterization and data assimilation of facies-based geomodels

arXiv: https://arxiv.org/abs/2406.14815 · HTML: https://mlsanity.com/paper/2406.14815/

## Key facts

- Cited by 4 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 15 of its 33 references that are in the map.
- First posted on arXiv 21 Jun 2024.

## 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, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Training-image based geostatistical inversion using a spatial generative adversarial neural network](https://mlsanity.com/paper/1708.04975/) (2017)
- [Parametric generation of conditional geological realizations using generative neural networks](https://mlsanity.com/paper/1807.05207/) (2018)
- [Towards a Robust Parameterization for Conditioning Facies Models Using Deep Variational Autoencoders and Ensemble Smoother](https://mlsanity.com/paper/1812.06900/) (2018)
- [3D CNN-PCA: A Deep-Learning-Based Parameterization for Complex Geomodels](https://mlsanity.com/paper/2007.08478/) (2020)
- [Recent Developments Combining Ensemble Smoother and Deep Generative Networks for Facies History Matching](https://mlsanity.com/paper/2005.10638/) (2020)
- [Latent Diffusion Model for Conditional Reservoir Facies Generation](https://mlsanity.com/paper/2311.01968/) (2023)
- [Data-Space Inversion Using a Recurrent Autoencoder for Time-Series Parameterization](https://mlsanity.com/paper/2005.00061/) (2020)

## Built on by (most cited first, 4 of 4)

- [Controlled Latent Diffusion Models for 3D Porous Media Reconstruction](https://mlsanity.com/paper/2503.24083/) (2025)
- [Diffusion models for multivariate subsurface generation and efficient probabilistic inversion](https://mlsanity.com/paper/2507.15809/) (2025)
- [3D latent diffusion models for parameterizing and history matching multiscenario facies systems](https://mlsanity.com/paper/2508.16621/) (2025)
- [Integrating Score-Based Diffusion Models with Machine Learning-Enhanced Localization for Advanced Data Assimilation in Geological Carbon Storage](https://mlsanity.com/paper/2511.05266/) (2025)

## Abstract (arXiv)

Geological parameterization entails the representation of a geomodel using a small set of latent variables and a mapping from these variables to grid-block properties such as porosity and permeability. Parameterization is useful for data assimilation (history matching), as it maintains geological realism while reducing the number of variables to be determined. Diffusion models are a new class of generative deep-learning procedures that have been shown to outperform previous methods, such as generative adversarial networks, for image generation tasks. Diffusion models are trained to "denoise", which enables them to generate new geological realizations from input fields characterized by random noise. Latent diffusion models, which are the specific variant considered in this study, provide dimension reduction through use of a low-dimensional latent variable. The model developed in this work includes a variational autoencoder for dimension reduction and a U-net for the denoising process. Our application involves conditional 2D three-facies (channel-levee-mud) systems. The latent diffusion model is shown to provide realizations that are visually consistent with samples from geomodeling software. Quantitative metrics involving spatial and flow-response statistics are evaluated, and general agreement between the diffusion-generated models and reference realizations is observed. Stability tests are performed to assess the smoothness of the parameterization method. The latent diffusion model is then used for ensemble-based data assimilation. Two synthetic "true" models are considered. Significant uncertainty reduction, posterior P10-P90 forecasts that generally bracket observed data, and consistent posterior geomodels, are achieved in both cases. PLEASE CITE AS: 10.1016/j.cageo.2024.105755 https://www.sciencedirect.com/science/article/pii/S0098300424002383 NOT WITH THE ARXIV VERSION