To address the challenges in integrating Digital-Twin (DT) technology with large-scale generative models in industrial design, a CAD-LDT digital-twin modeling framework based on generative foundation models was proposed. The framework adopted a triadic architecture consisting of a physical-entity module, an intelligent generation module, and a virtual-entity module, and innovatively incorporated multi-modal data fusion mechanisms and domain-knowledge constraints to enable autonomous generation of parameterized CAD models from physical-entity descriptions. Utilizing LLaVA-7B and LLaMA-7B as backbone models, the framework employed LoRA-based lightweight adapters to achieve cross-modal alignment between visual and textual features, and introduced a constraint encoder that transformed geometric tolerances and physical rules into structured JSON objects. To enhance the mathematical consistency of spatial transformations, Lie-group algorithms were adopted for the optimization of rigid-body transformations, while a geometric-weight binning strategy was proposed to discretize complex assembly relationships. Moreover, a spatiotemporal-decoupled generation strategy was designed to jointly optimize spatial layout and assembly sequencing. Experimental results on the DeepCAD dataset indicated that the proposed framework achieved an Intersection- over-Union (IoU) of 83.6%, a constraint satisfaction rate of 91.3%, and a 26.5% improvement in generation efficiency, significantly outperforming existing baseline models. Further ablation studies confirmed the critical contributions of multi-modal fusion, constraint encoding mechanisms, and Lie-group optimization to modeling performance, providing a novel DT modeling paradigm for intelligent manufacturing with demonstrated value in parametric design and assembly process optimization.