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

Abstract

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.