Story understanding and generation have long been a challenging task in natural language processing (NLP), especially when dealing with various levels of instruction specificity. In this paper, we propose a novel approach called "Weak to Strong Instruction Tuning" for improving story generation by tuning models with instructions of varying clarity. We explore the potential of large language models (LLMs) to adapt to different types of instructions, weak and strong, and show that our method significantly enhances performance in story comprehension and generation. By leveraging the strength of instruction tuning, we train models to understand the nuances of story plots, characters, and themes while generating coherent and engaging narratives. Through extensive experiments on several benchmark datasets and comparison with state-of-the-art baselines, we demonstrate that our method outperforms existing techniques, yielding substantial improvements in both automatic evaluation metrics and human evaluations. Our work shows that adaptive instruction tuning can be a powerful tool in refining generative models for complex narrative tasks.