Sketch–Solver: Decoupling Construction and Parameterization for Natural-Language CAD Program Synthesis

Natural-language CAD generation is commonly formulated as end-to-end translation, where a single decoder interleaves construction logic and numerical values within the same program sequence. This formulation imposes two distinct burdens: parameters must be chosen before the construction is complete, while repeated and related numerical occurrences are treated as independent predictions even when they correspond to fewer underlying degrees of freedom. Consequently, generation is vulnerable to structural errors and must recover parametric consistency through repeated autoregressive agreement. We propose Sketch-Solver, a framework that reorganizes both the generation process and the numerical representation. Its construction-parameter factorization separates construction from parameterization: Sketch generates a symbolic construction skeleton, andSolver subsequently instantiates the completed structure conditioned on both the instruction and the skeleton. Within this factorization interface, a constraint-aware reparameterization collapses repeated quantities into shared parameters and expresses selected proportional relations as executable dependencies, reducing unnecessary numerical decisions and yielding a canonical parameterization. Deterministic composition then produces the final executable CAD program. Experiments across multiple backbones and corpus-quality regimes show that Sketch-Solver improves synthesis robustness; controlled ablations separately identify the benefit of completed-construction conditioning and show that shared parameter names sharply reduce invalid and severe failures. The same framework also enables more reliable parameter-only editing through skeleton reuse. Together, these results show that decoupling construction from parameterization offers a new representation for CAD generation and an extensible interface for future methods.