Assembly-Relational Generative Modeling: Joint Generation of 3D Parts, Connection Interfaces, and Assembly Operations

Three-dimensional generative modeling has advanced through diffusion models, neural radiance fields, 3D Gaussian Splatting, and point-cloud generation. However, generating a collection of geometrically plausible components does not necessarily produce an object whose components can be physically connected, assembled in a feasible order, or operated according to its intended function. This paper proposes Assembly-Relational Generative Modeling (ARGM), a framework for generating three-dimensional objects through the joint modeling of component geometry, connection interfaces, relational structure, and assembly operations. Unlike approaches that treat assembly primarily as the placement of existing parts, ARGM represents connections as explicit generative variables that constrain and modify component geometry throughout the generation process. Each candidate object is represented by a typed assembly graph whose nodes encode component geometry and whose edges encode connection mechanisms, interface parameters, relative poses, and operational constraints. A connection-conditioned geometric generator produces compatible interfaces, while a constraint-aware relational optimizer refines component configurations and an operation planner generates a feasible assembly sequence. The framework supports insertion, welding, adhesive bonding, bolted fastening, and other connection mechanisms through a shared representation with mechanism-specific constraints. A multi-objective training formulation combines geometric reconstruction, interface compatibility, structural connectivity, collision avoidance, assembly feasibility, and task-dependent functional requirements. We also define evaluation protocols for geometric quality, connection validity, assembly feasibility, and robustness to component perturbations. ARGM is presented as a testable research framework rather than an empirically validated system. Its principal research hypothesis is that jointly generating component geometry and connection relations can improve the physical and operational validity of generated 3D assemblies compared with pipelines that optimize component shapes and placements independently.