<p>Globally, wind is one of the fastest growing renewable energy sources, requiring innovative computational methods across the spectrum of wind energy engineering tasks to boost wind energy production. Recent advancements in generative artificial intelligence (AI) models have led to the integration of the models into wind energy engineering to develop solutions. Previous surveys primarily focused on the general applications of AI in wind energy. The objectives of this survey are to: (i) review modified generative AI models in wind energy engineering tasks, (ii) develop taxonomy linking model variants to tasks, (iii) develop performance evaluation metrics taxonomy, (iv) analyze the core concepts and limitations of the modified generative AI models, (v) examine data sources, (vi) present real-world case studies, (vii) identify emerging trends and challenges. This is the first comprehensive survey exclusively for modified generative AI models across different aspects of wind energy engineering. The survey examines the modifications of generative AI models for wind energy applications, explaining the core idea behind each modification, its suitability for specific task and the limitations identified in the corresponding model. New taxonomies were introduce to support synthesis and analysis. The survey extends beyond theoretical discussion by highlighting real-world case studies where generative AI models have been deployed in real-world commercial wind farms. Additionally, emerging open challenges are identified and future research directions are proposed from new perspectives. This survey provide a fundamental reference for early career researchers, a guide to industry practitioners and a benchmark for innovations for expert researchers.</p>