The inverse design of architected metamaterials with targeted nonlinear mechanical behavior remains a major challenge especially in the presence of large deformations, buckling, contact, and plasticity, as well as limitations in existing geometry representations. Most current inverse design approaches rely on binary pixel or voxel descriptions, which introduce jagged boundaries, complicate finite element (FE) simulations, and hinder manufacturability. In this work, we present a data-driven, closed-loop framework for metamaterial inverse design and forward evaluation that overcomes these limitations. Our approach employs an implicit signed distance function (SDF) to represent metamaterial geometries, providing smooth, high-fidelity boundaries that are directly compatible with FE analysis and additive manufacturing without post-processing. A classifier-free guided conditional diffusion model is trained to generate SDF-based unit cell architectures conditioned on target macroscopic nonlinear stress–strain curves, enabling efficient one-shot inverse design and one-to-many solution synthesis. To evaluate the mechanical performance of the generated designs without repeated costly simulations, we introduce a Neural Operator Transformer (NOT) as a forward surrogate model. The NOT accurately predicts both homogenized constitutive responses and full-field solution quantities on irregular, unstructured meshes, demonstrating strong generalization across arbitrary geometries. To illustrate the capabilities of the multiscale design framework, we investigate the design of a two-phase metamaterial whose nonlinear compressive response involves the combined contributions of large deformations, plasticity, and self-contact. The proposed framework enables rapid generation, validation, and exploration of nonlinear metamaterial designs within a unified pipeline. By integrating smooth geometric representations, diffusion-based generative modeling, and transformer-based neural operators, this work establishes a scalable pathway for designing advanced metamaterials with customized mechanical performance. REFERENCE Liu, Q., Koric, S., Abueidda, D., Meidani, H., and Geubelle, P. H. (2025) “Toward signed distance function-based metamaterial design: neural operator transformer for forward prediction and diffusion models for inverse design”. Computational Methods in Applied Mechanics and Engineering, 446B, 118316. https://doi.org/10.1016/j.cma.2025.118316.