# 3D latent diffusion models for parameterizing and history matching multiscenario facies systems

arXiv: https://arxiv.org/abs/2508.16621 · HTML: https://mlsanity.com/paper/2508.16621/

## Key facts

- Cited by 1 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 16 of its 49 references that are in the map.
- First posted on arXiv 14 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, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [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)
- [Latent diffusion models for parameterization and data assimilation of facies-based geomodels](https://mlsanity.com/paper/2406.14815/) (2024)
- [Likelihood-Free Inference and Hierarchical Data Assimilation for Geological Carbon Storage](https://mlsanity.com/paper/2410.15302/) (2024)

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

- [Differentiable Inverse Modeling with Physics-Constrained Latent Diffusion for Heterogeneous Subsurface Parameter Fields](https://mlsanity.com/paper/2512.22421/) (2025)

## Abstract (arXiv)

Geological parameterization procedures entail the mapping of a high-dimensional geomodel to a low-dimensional latent variable. These parameterizations can be very useful for history matching because the number of variables to be calibrated is greatly reduced, and the mapping can be constructed such that geological realism is automatically preserved. In this work, a parameterization method based on generative latent diffusion models (LDMs) is developed for 3D channel-levee-mud systems. Geomodels with variable scenario parameters, specifically mud fraction, channel orientation, and channel width, are considered. A perceptual loss term is included during training to improve geological realism. For any set of scenario parameters, an (essentially) infinite number of realizations can be generated, so our LDM parameterizes over a very wide model space. New realizations constructed using the LDM procedure are shown to closely resemble reference geomodels, both visually and in terms of one- and two-point spatial statistics. Flow response distributions, for a specified set of injection and production wells, are also shown to be in close agreement between the two sets of models. The parameterization method is applied for ensemble-based history matching, with model updates performed in the LDM latent space, for cases involving geological scenario uncertainty. For three synthetic true models corresponding to different geological scenarios, we observe clear uncertainty reduction in both production forecasts and geological scenario parameters. The overall method is additionally shown to provide posterior geomodels consistent with the synthetic true model in each case.