To address the challenges of design space exploration and limited representation in the inverse design of complex structures under multi-objective performance constraints, this paper proposes a unified framework integrating multi-dimensional generative paradigms. At the pixel level, pixel generation models are employed to capture the fine-grained features of material distribution, establishing a direct mapping from performance space to pixel density fields for rapid topological evolution. Extending to the lattice structure level, the framework incorporates graph generation models to precisely characterize the topological connectivity of unit cells, effectively solving the inverse problem for functionally graded metamaterials in discrete spaces. Furthermore, to achieve explicit geometric representation, a language generation mechanism is introduced in conjunction with the Moving Morphable Components (MMC) method, translating complex geometric topologies into interpretable, structured semantic sequences. By integrating cross-dimensional strategies spanning from discrete pixel configuration and graph-based topological representation to explicit semantic description, this approach overcomes the limitations of single representation methods. It significantly enhances optimization efficiency and manufacturability under multi-objective constraints, offering a novel theoretical perspective and technical pathway for the intelligent design of high-performance structures.