Abstract: Recovering editable 3D parametric curves from 2D images is a fundamental challenge in computer graphics, bridging pixel-based perception and vector-based CAD modeling. Existing NeRF- and 3DGS-based methods often rely on dense calibrated views, precomputed 2D edge maps, and costly per-scene optimization, limiting their applicability to casually captured real-world inputs. We propose CGGT, a Curve-Grounded Geometry Transformer that directly grounds 3D-consistent 2D curve instances in the image space from sparse, unposed multi-view images. CGGT combines a geometry-aware transformer encoder for multi-view feature learning with a curve-aware masked-attention decoder for cross-view instance association. In a single forward pass, it predicts camera parameters, dense depth maps, and instance-level 2D curve masks, which are then lifted into 3D and refined through a fast parametric optimization stage to recover compact, editable 3D curve primitives. To support structured curve learning, we introduce Wireframe-100K, a large-scale dataset comprising 100,000 CAD models with diverse topologies, realistic multi-view renderings, and accurate parametric curve annotations. Extensive experiments show that our framework achieves substantial improvements in both reconstruction accuracy and efficiency, particularly under challenging sparse-view settings and in separating persistent 3D structural edges from view-dependent image edges caused by silhouettes, textures, and appearance variations. Despite being trained solely on synthetic data, CGGT generalizes well to real-world images, demonstrating its potential for practical CAD-style wireframe reconstruction from unconstrained visual inputs.