CADMate: Generating CAD Assembly Plan with Geometric Chain-of-Thought and Spatial Physical Rewards

Computer-aided design (CAD) is crucial in prototyping complex 3D objects through precise geometric modeling. In practical design workflows, designers manually define assembly sequences for individual CAD parts, a process that is both time-consuming and expertiseintensive. To address this challenge, we formulate CAD assembly as a parametric action prediction task: given a reference design image and disassembled parts, the model predicts 6-DoF transformations (i.e., actions) to progressively assemble each part. This paradigm enables multimodal large language models (MLLMs) to solve the task through autoregressive action generation. While recent MLLMs demonstrate promising spatial reasoning, they struggle with fine-grained geometric structure understanding and physical collision avoidance during assembly. In this paper, we propose CADMATE, an MLLM-based framework for sequential CAD assembly action generation. Our training strategy comprises three stages: (i) CAD domain adaptation for spatial geometry and position understanding, (ii) supervised fine-tuning with geometric chain-ofthought (CoT) reasoning for action generation, and (iii) reinforcement learning with spatialphysical rewards jointly optimize spatial accuracy and collision avoidance. Additionally, we also construct CADBuilder dataset, comprising over 45K CAD assemblies with annotated action sequences. Our experiments demonstrate that CADMATE significantly outperforms existing prominent MLLMs (e.g., GPT-5), showing great potential in design applications 1 .