Generative AI models are highly susceptible to adversarial attacks and are primarily employed for various use cases in cloud environments. These are subtle manipulations but can successfully leverage model vulnerabilities, hence posing critical security challenges when these models are exposed in shared multi-tenant cloud infrastructures. These could result in compromised outputs, model performance degradation, and eventual sensitive data breaches. This work studies vulnerabilities that generative AI models, especially those in the cloud, have due to unique infrastructure characteristics that amplify adversaries in their threat exposure. It first identifies core generative AI architecture weaknesses that make them vulnerable to those attacks. Then, it describes model testing and behavior-tracking frameworks for simulation, analysis, and understanding of adversarial attacks. It is followed by an in-depth review of state-of-the-art defense mechanisms, namely adversarial training, input sanitization, and robust design techniques, evaluated against their pros and cons concerning generative model protection. This work insists on a multi-layered defense strategy that combines cloud-specific security measures with model-based countermeasures, which will mitigate the risks effectively. It discusses future challenges by calling for adaptive security solutions and furthering standardized protocols for improved resilience from specified, constantly evolving adversarial threats in cloud-hosted generative AI. The knowledge captured will go a long way in designing more secure AI systems that can withstand adversarial manipulation while retaining performance integrity.