The discovery of novel functional molecules is a critical bottleneck in addressing global challenges, ranging from life-threatening diseases to climate change. The chemical space of potential drug-like and material candidates is vast, with at over 1060 structures; however, traditional discovery pipelines rely on the slow iterative screening of existing libraries. This study presents a unified Inverse Design framework utilizing Generative Artificial Intelligence (GAI) to accelerate the discovery of therapeutic small molecules and Metal-Organic Frameworks (MOFs) for carbon capture. We employed deep generative models, specifically Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs), to construct novel molecular structures optimized for specific target properties. For pharmaceutical applications, the models were conditioned to generate compounds with high binding affinities for oncology targets and low toxicities. Simultaneously, in materials science, the framework was applied to design MOFs with maximized CO₂ adsorption capacity and selectivity. We validated the generated structures using computational simulations, including molecular docking of drug candidates and Grand Canonical Monte Carlo (GCMC) simulations of MOFs. Our results demonstrate that generative models successfully navigate the chemical space to produce valid, synthesizable, and high-performance candidates that outperform those obtained through random sampling. This study highlights the versatility of Generative AI as a platform technology capable of significantly reducing the time and cost associated with the hit-to-lead phase in both pharmaceutical R&D and materials engineering.