# Well2Flow: Reconstruction of reservoir states from sparse wells using score-based generative models

arXiv: https://arxiv.org/abs/2504.06305 · HTML: https://mlsanity.com/paper/2504.06305/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 4 of its 9 references that are in the map.
- First posted on arXiv 7 Apr 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, 4 of 4)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)

## Abstract (arXiv)

This study investigates the use of score-based generative models for reservoir simulation, with a focus on reconstructing spatially varying permeability and saturation fields in saline aquifers, inferred from sparse observations at two well locations. By modeling the joint distribution of permeability and saturation derived from high-fidelity reservoir simulations, the proposed neural network is trained to learn the complex spatiotemporal dynamics governing multiphase fluid flow in porous media. During inference, the framework effectively reconstructs both permeability and saturation fields by conditioning on sparse vertical profiles extracted from well log data. This approach introduces a novel methodology for incorporating physical constraints and well log guidance into generative models, significantly enhancing the accuracy and physical plausibility of the reconstructed subsurface states. Furthermore, the framework demonstrates strong generalization capabilities across varying geological scenarios, highlighting its potential for practical deployment in data-scarce reservoir management tasks.