Despite the rapid advancements in generative AI, the integration of Large Language Models (LLMs) with diffusion models remains an underexplored domain, with significant potential for transformative applications across multimodal tasks. This survey addresses this critical gap by providing a comprehensive analysis of recent progress in this integration. Methodologically, the study examines approaches like latent space alignment, prompt engineering, and novel architectures that foster synergy between LLMs and diffusion models. Key findings reveal that while this integration enhances generative capabilities, it introduces challenges, including high computational costs, misalignment of model modalities, data scarcity, and quality control issues. The survey systematically evaluates existing solutions to these challenges, highlighting their strengths, limitations, and practical implications. Emerging trends such as efficient fine-tuning strategies, hybrid architectures, and multimodal data augmentation are identified as promising avenues for future research. By synthesizing current knowledge and offering actionable insights, this survey serves as a valuable resource for researchers and practitioners seeking to explore the combined potential of LLMs and diffusion models. The repository for this survey is publicly available at https://github.com/AnasHXH/Connecting-LLMs-to-Diffusion-Models-A-Survey.