  Recent advancements in artificial intelligence (AI)-based design strategies
for metamaterials have revolutionized the creation of customizable
architectures spanning nano- to macro-scale dimensions, achieving unprecedented
mechanical behaviors that surpass the inherent properties of the constituent
materials. However, the growing complexity of these methods poses challenges in
generating diverse metamaterials without substantial human and computational
resources, hindering widespread adoption. Addressing this, our study introduces
an innovative design strategy capable of generating various three-dimensional
graph metamaterials using simple arithmetic operations within the latent space.
By seamlessly integrating hidden representations of disentangled latent space
and latent diffusion processes, our approach provides a comprehensive
understanding of complex design spaces, generating diverse graph metamaterials
through arithmetic operations. This methodology stands as a versatile tool for
creating structures ranging from repetitive lattice structures to functionally
graded mechanical metamaterials. It also serves as an inverse design strategy
for diverse lattice structures, including crystalline structures and those made
of trabecular bone. We believe that this methodology represents a foundational
step in advancing our comprehension of the intricate latent design space,
offering the potential to establish a unified model for various traditional
generative models in the realm of mechanical metamaterials.
