Efficient CO2 capture is vital for mitigating climate change, with amine-based solvents being widely used due to their strong reactivity with CO2. However, optimizing key properties such as basicity, viscosity, and absorption capacity remains challenging, as traditional methods rely on labor-intensive experimentation and predefined chemical databases, limiting the exploration of novel solutions. Here, SAGE-Amine was introduced, a generative modeling approach that integrates Scoring-Assisted Generative Exploration (SAGE) with quantitative structure-property relationship models to design new amines tailored for CO2 capture. Unlike conventional virtual screening restricted to existing compounds, SAGE-Amine generates novel amines by leveraging autoregressive natural language processing models trained on amine datasets. SAGE-Amine identified known amines for CO2 capture from scratch and successfully performed single-property optimization, increasing basicity or reducing viscosity or vapor pressure. Furthermore, it facilitated multi-property optimization, simultaneously achieving high basicity with low viscosity and vapor pressure. The 10 top-ranked amines were suggested using SAGE-Amine and their thermodynamic properties were further assessed using COSMO-RS simulations, confirming their potential for CO2 capture. These results highlight the potential of generative modeling in accelerating the discovery of amine solvents and expanding the possibilities for industrial CO2 capture applications.