Physically Aware Generative Design for Spatial Mechanism Synthesis: A Differentiable Diffusion-Refinement Framework

Abstract

Spatial mechanism synthesis requires joint reasoning over discrete topology and continuous geometry under strict loop-closure constraints. Existing search-based methods are often tied to predefined topology spaces, while purely data-driven generators can produce topologically plausible but kinematically infeasible mechanisms. This paper proposes GenRefMechSyn, a physics-aware generative framework that integrates Mimic, a Diffusion Transformer (DiT)-based topology–geometry sketch generator, Refiner, a differentiable kinematic refiner, and Judge, a refinement-aware value model. Mimic proposes candidate mechanism sketches, Refiner optimizes continuous geometry under fixed topology and projects candidates toward the kinematic-feasibility region, and Judge uses refinement feedback to guide diffusion sampling toward candidates with higher downstream refinability. Under a 1000-trial acceptance protocol, GenRefMechSyn achieves 81.6% two-translational-DOF (2T) kinematic validity; controlled baselines obtain 6.6% for DiT+Refiner without Judge guidance/feedback augmentation, 84.3% for genetic algorithm (GA)+Refiner with a favorable fixed topology, and 12.2% for multi-topology GA+Refiner. The generated mechanisms reach loop-closure residuals and task errors on the order of $10^{-3}$ and $10^{-4}$, respectively. The same architecture and seed set are also used in an independently trained two-rotational-DOF (2R) feedback run, showing applicability to a separately trained rotational task.