StepCAD: Mesh-to-CAD Code Generation via LLM Policy and Geometry-Guided Search

Recovering executable CAD programs from 3D meshes is fundamentally challenging due to the long-horizon, compositional nature of CAD construction and the need for precise estimation of both discrete operations and continuous parameters. Existing learning-based methods primarily treat mesh-to-CAD reconstruction as one-shot sequence prediction and are largely limited to simple sketch-extrude pipelines, restricting operation diversity and preventing the use of intermediate geometric feedback, with no mechanism for refining generated programs. To address this limitation, we introduce StepCAD, a generative optimization approach that performs step-by-step, geometry-conditioned program synthesis followed by explicit refinement in program space. Given an input mesh, StepCAD first predicts construction sequences using a state-conditioned CAD policy conditioned on both target and intermediate geometry, then refines them through IoU-guided tree search over local program edits. To address the limited operation diversity in prior work, we further introduce ARCADE-1.5M, a large-scale dataset of 1.5M executable CAD programs with diverse operations, long-horizon sequences up to 150+ operations, and 12.5M intermediate state-action transitions. Experiments on multiple CAD reconstruction benchmarks show that StepCAD achieves state-of-the-art reconstruction accuracy, validity, and robustness, with up to 87.2\% relative IoU improvement over the best prior method and increasingly larger gains as shape complexity increases.