# Integrating Score-Based Diffusion Models with Machine Learning-Enhanced Localization for Advanced Data Assimilation in Geological Carbon Storage

arXiv: https://arxiv.org/abs/2511.05266 · HTML: https://mlsanity.com/paper/2511.05266/

## 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 22 of its 68 references that are in the map.
- First posted on arXiv 7 Nov 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, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [Why do tree-based models still outperform deep learning on tabular data?](https://mlsanity.com/paper/2207.08815/) (2022)
- [Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2001.01520/) (2020)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)
- [Combining data assimilation and machine learning to infer unresolved scale parametrisation](https://mlsanity.com/paper/2009.04318/) (2020)
- [Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization](https://mlsanity.com/paper/2001.06270/) (2020)
- [Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components](https://mlsanity.com/paper/2102.07819/) (2021)
- [A comparison of combined data assimilation and machine learning methods for offline and online model error correction](https://mlsanity.com/paper/2107.11114/) (2021)
- [An uncertainty-aware Digital Shadow for underground multimodal CO2 storage monitoring](https://mlsanity.com/paper/2410.01218/) (2024)
- [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)

- [Data assimilation for subsurface flow using latent diffusion model parameterization: performance of ensemble-Kalman and Monte Carlo techniques](https://mlsanity.com/paper/2606.11140/) (2026)

## Abstract (arXiv)

Accurate characterization of subsurface heterogeneity is important for the safe and effective implementation of geological carbon storage (GCS) projects. This paper explores how machine learning methods can enhance data assimilation for GCS with a framework that integrates score-based diffusion models with machine learning-enhanced localization in channelized reservoirs during CO2 injection. We employ a machine learning-enhanced localization framework that uses large ensembles (Ns = 5000) with permeabilities generated by the diffusion model and states computed by simple ML algorithms to improve covariance estimation for the Ensemble Smoother with Multiple Data Assimilation (ESMDA). We apply ML algorithms to a prior ensemble of channelized permeability fields, generated with the geostatistical model FLUVSIM. Our approach is applied on a CO2 injection scenario simulated using the Delft Advanced Research Terra Simulator (DARTS). Our ML-based localization maintains significantly more ensemble variance than when localization is not applied, while achieving comparable data-matching quality. This framework has practical implications for GCS projects, helping improve the reliability of uncertainty quantification for risk assessment.