Generative AI creates new material, including text and images, by identifying patterns and data from large datasets. This chapter uses mathematical models like deep neural networks, which leverage probabilistic frameworks and intricate architectures. These models simulate the creative processes observed in human cognition. Key concepts covered in this chapter include probability distributions, optimization algorithms, and complex neural network architectures. These elements enable AI systems to generate original content rather than merely repeating learned examples. This chapter provides a comprehensive insight into the mathematical models of generative AI and the role of deep neural networks. This chapter also discusses various neural network architectures essential in generative AI, such as transformers, generative adversarial networks (GANs), and diffusion models.