# Generative Geostatistical Modeling from Incomplete Well and Imaged Seismic Observations with Diffusion Models

arXiv: https://arxiv.org/abs/2406.05136 · HTML: https://mlsanity.com/paper/2406.05136/

## 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 0 of its 1 references that are in the map.
- First posted on arXiv 16 May 2024.

## Placed in

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

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

- [Machine learning-enabled velocity model building with uncertainty quantification](https://mlsanity.com/paper/2411.06651/) (2024)
- [OpenSeisML: Open Large-Scale Real Seismic and well-log Dataset for Generative AI](https://mlsanity.com/paper/2605.20539/) (2026)
- [SAGE: Subsurface AI-driven Geostatistical Extraction with proxy posterior](https://mlsanity.com/paper/2604.00307/) (2026)
- [Observation-Aligned Mask Priors for Learning Physical Fields from Authentic Occlusions](https://mlsanity.com/paper/2605.16818/) (2026)

## Abstract (arXiv)

In this study, we introduce a novel approach to synthesizing subsurface velocity models using diffusion generative models. Conventional methods rely on extensive, high-quality datasets, which are often inaccessible in subsurface applications. Our method leverages incomplete well and seismic observations to produce high-fidelity velocity samples without requiring fully sampled training datasets. The results demonstrate that our generative model accurately captures long-range structures, aligns with ground-truth velocity models, achieves high Structural Similarity Index (SSIM) scores, and provides meaningful uncertainty estimations. This approach facilitates realistic subsurface velocity synthesis, offering valuable inputs for full-waveform inversion and enhancing seismic-based subsurface modeling.