Attention-Guided Flow-Matching for Sparse 3D Geological Generation
Authors: Zhixiang Lu, Mengqi Han, Peixin Guo, Tianming Bai, Jionglong Su, Fei Fang, Sifan Song
Organizations: Xi’an Jiaotong-Liverpool University, Jiangsu 215123, China · Deep Optica, Shanghai 200030, China · University of Chinese Academy of Sciences, Beijing 100049, China
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.
Figures & tables
Figure 1: The architecture of Attention-Guided Continuous Flow-Matching (3D-GeoFlow) model.
Figure 2: Detailed architecture of the 3D Spatial Attention Gates (3D-SAG). This mechanism spatially filters skip-connection features, compelling the model to focus on the long-range structural continuity implied by the sparse borehole conditions while suppressing unexplored noise regions.
Method
Acc (Incl. Air)
Acc (Excl. Air)
mIoU (Excl. Air)
Rule-based Deterministic Baselines
Depth-wise Majority [ 18 ]
52.81%
17.55%
5.36%
Polygonal Method [ 21 ]
53.07%
18.00%
5.73%
Standard Deep Generative Baselines
Diffusion (DDPM) [ 9 ]
48.82%
10.57%
4.65%
Flow-Matching [ 12 ]
74.17%
54.87%
27.51%
Table 1: Out-Of-Distribution Performance Comparison of 3D Geological Modeling Methods.
Geological Class
Proportion (%)
Baseline (Standard FM)
3D-GeoFlow (Attention-Guided)
Acc (%)
IoU (%)
Acc (%)
IoU (%)
01 Air
42.77
100.00
99.99
100.00
100.00
04 Mt Janet Andesite
19.76
53.66
45.01
84.67
70.08
02 Molly Darling Sandstone
17.33
64.37
60.35
81.93
75.81
07 Surface Sand / Soil
7.66
61.66
54.85
59.05
56.50
03 Ignimbrite
5.73
45.97
20.85
49.58
29.80
Table 2: Quantitative Evaluation of Per-Class Performance. We report the Accuracy (Acc) and Intersection over Union (IoU) for the geological classes. Best results are highlighted in bold .
Figure 3: Qualitative 3D rendering results on the Out-Of-Distribution (OOD) test set.
Figure 4: Training and validation loss curves over epochs between 3D-GeoFlow (Proposed) and flow-matching (Baseline) model.
Flow-based generative modeling learns probability transports from simple noise to data for fast sampling, density estimation, and controllable generation.
Scaling image-to-3D generation to ultra-high resolutions requires controlling rapidly growing computational costs without sacrificing fine geometric detail. We present Filigree3D, a sparse latent flow-matching framework that generates 3D geometry from a single image at voxel resolutions up to 20483, with straightforward extensibility to 40963. To make training tractable, we introduce Structure-Aware Sparse Scaling, which combines spatial bounding with alternating local-global attention to constrain token growth while preserving both fine-scale details and long-range structural context. To enhance detail reconstruction, we curate training samples based on their high-resolution geometric gains and inject multi-scale image features into a sparse 3D DiT, effectively coupling structural semantics with fine-grained visual cues. Furthermore, a visibility-aware voxel regularization strategy improves robustness against sparse perturbations and facilitates the completion of unobserved geometry. Under our default configuration, Filigree3D maintains peak GPU memory consumption within practical limits for contemporary hardware, enabling the generation of highly intricate 3D geometry in approximately one minute. Extensive experiments demonstrate that our method yields substantial improvements in overall geometric fidelity and fine-detail preservation compared to existing baselines, validating practical, detail-preserving 3D generation at unprecedented resolutions.
Sparse-view 3D modeling represents a fundamental tension between reconstruction fidelity and generative plausibility. While feed-forward reconstruction excels in efficiency and input alignment, it often lacks the global priors needed for structural completeness. Conversely, diffusion-based generation provides rich geometric details but struggles with multi-view consistency. We present RecGen3D, a framework that combines these two paradigms into a cooperative system. To overcome inherent conflicts in coordinate spaces, 3D representations, and training objectives, we align both models within a shared canonical space. We employ decoupled cooperative learning, which maintains stable training while enabling seamless collaboration during inference. Specifically, the reconstruction module is adapted to provide canonical geometric anchors, while the diffusion generator leverages latent-augmented conditioning to refine and complete the geometric structure. Experimental results demonstrate that RecGen3D achieves superior fidelity and robustness, outperforming existing methods in creating complete and consistent 3D models from sparse observations.
Zhisheng Huang, Jiahao Chen, Cheng Lin +10
Texas A&M University, College Station, USA · Macau University of Science and Technology, Macau, Macau · HKUST, Hong Kong, Hong Kong +2
Sparse voxel representation has emerged as a scalable foundation for image-to-3D Gaussian Splatting (3DGS) generation, yet current methods struggle to preserve high-frequency visual details of input images due to two structural bottlenecks. First, they adopt discriminative 2D features optimized for semantic abstraction to construct sparse voxel latents, which suppress reconstructive cues and induce a representation bottleneck. Second, in the generation stage, standard diffusion transformers lack effective mechanisms to align dense 2D image tokens with sparse 3D voxel latents, resulting in a cross-modal correspondence bottleneck. To address these issues, we propose FLUX3D, a scalable image-to-3DGS framework that boosts both representation learning and cross-modal alignment during generation. We first revisit 2D feature selection for sparse-voxel-based 3D representation learning, propose Diffusion-Aligned Structured Latents (DA-SLAT) and couple it with a decoder-only architecture to improve 3DGS reconstruction fidelity. We also design a sparse-structure-aware diffusion framework, which integrates the Sparse-structure Multimodal Diffusion Transformer (SMDiT) and Modal-Aware Rotary Positional Embedding (MARoPE) to achieve geometry-agnostic 2D-3D alignment. Extensive benchmark experiments demonstrate that FLUX3D yields substantial improvements in appearance fidelity and significantly outperforms all state-of-the-art (SOTA) methods in generating high-quality 3DGS assets.