This paper explores the integration of Generative Artificial Intelligence (GAI) into blockchain technology to address key challenges such as scalability, security, privacy, and interoperability. The authors introduce GAI techniques, outline their applications, and discuss existing solutions for integrating GAI into blockchains. They highlight the effectiveness of GAI in detecting unknown attacks, designing key secret sharing schemes, and enhancing privacy. A case study demonstrates how the Generative Diffusion Model (GDM) can optimize blockchain network performance metrics, showing faster convergence, higher rewards, and improved throughput and latency compared to traditional AI approaches. The paper also discusses future research directions, including personalized GAI-enabled blockchains, GAI-blockchain synergy, and privacy and security considerations within blockchain ecosystems.This paper explores the integration of Generative Artificial Intelligence (GAI) into blockchain technology to address key challenges such as scalability, security, privacy, and interoperability. The authors introduce GAI techniques, outline their applications, and discuss existing solutions for integrating GAI into blockchains. They highlight the effectiveness of GAI in detecting unknown attacks, designing key secret sharing schemes, and enhancing privacy. A case study demonstrates how the Generative Diffusion Model (GDM) can optimize blockchain network performance metrics, showing faster convergence, higher rewards, and improved throughput and latency compared to traditional AI approaches. The paper also discusses future research directions, including personalized GAI-enabled blockchains, GAI-blockchain synergy, and privacy and security considerations within blockchain ecosystems.