This paper explores the critical transition from Generative Artificial Intelligence (GenAI) to Innovative Artificial Intelligence (InAI). While recent advancements in GenAI have enabled systems to produce high-quality content across various domains, these models often lack the capacity for true innovation. In this context, innovation is defined as the ability to generate novel and useful outputs that go beyond mere replication of learned data. The paper examines this shift and proposes a roadmap for developing AI systems that can generate content and engage in autonomous problem-solving and creative ideation. The work provides both theoretical insights and practical strategies for advancing AI to a stage where it can genuinely innovate, contributing meaningfully to science, technology, and the arts.