# Attention-Guided Flow-Matching for Sparse 3D Geological Generation

arXiv: https://arxiv.org/abs/2604.09700 · HTML: https://mlsanity.com/paper/2604.09700/

## 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 11 of its 24 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## 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, 11 of 11)

- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Training-image based geostatistical inversion using a spatial generative adversarial neural network](https://mlsanity.com/paper/1708.04975/) (2017)
- [DeepGB-TB: A Risk-Balanced Cross-Attention Gradient-Boosted Convolutional Network for Rapid, Interpretable Tuberculosis Screening](https://mlsanity.com/paper/2508.02741/) (2025)
- [Causal-SAM-LLM: Large Language Models as Causal Reasoners for Robust Medical Segmentation](https://mlsanity.com/paper/2507.03585/) (2025)
- [SkinCLIP-VL: Consistency-Aware Vision-Language Learning for Multimodal Skin Cancer Diagnosis](https://mlsanity.com/paper/2603.21010/) (2026)
- [PRISM: A Personality-Driven Multi-Agent Framework for Social Media Simulation](https://mlsanity.com/paper/2512.19933/) (2025)
- [Synthetic Geology: Structural Geology Meets Deep Learning](https://mlsanity.com/paper/2506.11164/) (2025)

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

- [GeoCFM: Positive-Only Conditional Flow Matching for Mineral Occurrence Sampling](https://mlsanity.com/paper/2609.34398/) (2026)

## Abstract (arXiv)

Constructing high-resolution 3D geological models from sparse 1D borehole and 2D surface data is a highly ill-posed inverse problem. Traditional heuristic and implicit modeling methods fundamentally fail to capture non-linear topological discontinuities under extreme sparsity, often yielding unrealistic artifacts. Furthermore, while deep generative architectures like Diffusion Models have revolutionized continuous domains, they suffer from severe representation collapse when conditioned on sparse categorical grids. To bridge this gap, we propose 3D-GeoFlow, the first Attention-Guided Continuous Flow Matching framework tailored for sparse multimodal geological modeling. By reformulating discrete categorical generation as a simulation-free, continuous vector field regression optimized via Mean Squared Error, our model establishes stable, deterministic optimal transport paths. Crucially, we integrate 3D Attention Gates to dynamically propagate localized borehole features across the volumetric latent space, ensuring macroscopic structural coherence. To validate our framework, we curated a large-scale multimodal dataset comprising 2,200 procedurally generated 3D geological cases. Extensive out-of-distribution (OOD) evaluations demonstrate that 3D-GeoFlow achieves a paradigm shift, significantly outperforming heuristic interpolations and standard diffusion baselines.