The integration of Artificial Intelligence (AI) into cloud computing represents a pivotal shift in the technological landscape, offering unprecedented opportunities for innovation across industries. Deploying AI applications at scale on the cloud poses unique challenges, necessitating the development of scalable cloud architectures tailored to meet the computational demands and data processing needs inherent to AI. This article explores the foundational aspects of cloud computing architectures, emphasizing the principles of scalability essential for AI applications. It delves into the core challenges faced when deploying AI on the cloud, such as computational requirements, data management, network constraints, and security concerns. Further, it presents various architectural models that facilitate scalability, including containerization, serverless computing, and cloud-native AI services, drawing from realworld case studies to illustrate effective strategies and best practices. Additionally, the article examines performance optimization techniques, security considerations, and the future directions of cloud-based AI deployments, highlighting the role of emerging technologies such as quantum computing and edge AI. By providing a comprehensive overview of scalable cloud architectures for AI applications, this article aims to guide researchers, practitioners, and organizations in leveraging cloud computing to its full potential, thereby enabling more efficient, secure, and scalable AI solutions.