Generative modeling within supply chain management reveals significant potential for enhancing operational efficiency, adaptability, and resilience. Leveraging advanced AI-driven methods such as Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and autoregressive models, this paper investigates their role in transforming demand forecasting, inventory management, logistics optimization, and risk mitigation. By simulating complex scenarios and capturing dynamic data relationships, these models enable organizations to predict disruptions, optimize inventory levels, and streamline logistics, reducing operational costs and improving responsiveness. This study systematically examines the capabilities of generative models in addressing inefficiencies in traditional supply chains. It demonstrates how GANs mitigate stockout risks by improving demand predictions. VAEs enhance supply chain transparency through latent variable modeling, and autoregressive models forecast time-series data to refine inventory and production planning. Additionally, generative approaches integrate real-time data to dynamically optimize routing and decision-making under uncertainty. Despite their transformative potential, the paper identifies persistent barriers, including data quality issues, interpretability challenges, and integration complexities. To overcome these, it proposes leveraging federated generative models for secure, decentralized collaboration and embedding sustainability metrics into generative frameworks for eco-conscious supply chain management. This work underscores the necessity of integrating generative modeling as a core strategy to drive efficiency, agility, and resilience in modern supply chain systems.