This paper presents CodeRefine, a novel framework for automatically transforming research paper methodologies into functional code using Large Language Models (LLMs). Our multi-step approach first extracts and summarizes key text chunks from papers, analyzes their code relevance, and creates a knowledge graph using a predefined ontology. Code is then generated from this structured representation and enhanced through a proposed retrospective retrieval-augmented generation approach. CodeRefine addresses the challenge of bridging theoretical research and practical implementation, offering a more accurate alternative to LLM zero-shot prompting. Evaluations on diverse scientific papers demonstrate CodeRefine's ability to improve code implementation from the paper, potentially accelerating the adoption of cutting-edge algorithms in real-world applications.