Fine-tuning large language models (LLMs) for specific tasks requires high-quality, diverse training data relevant to the task. Recent research has leveraged LLMs to synthesize training data, but existing approaches either depend on large seed datasets or struggle to ensure both task relevance and data diversity in the generated outputs. To address these challenges, we propose AIDE, a novel data synthesis framework that uses a multi-hop process to expand 10 seed data points while ensuring diversity and task relevance. AIDE extracts the main topic and key knowledge attributes from the seed data to guide the synthesis process. In each subsequent hop, it extracts the topic and attributes from the newly generated data and continues guided synthesis. This process repeats for a total of K hops. To prevent irrelevant data generation as the hop depth increases, AIDE incorporates a residual connection mechanism and uses self-reflection to improve data quality. Our empirical results demonstrate that fine-tuning Mistral-7B, Llama-3.1-8B and Llama-3.2-3B with AIDE achieves more than 10% accuracy improvements over the base models across 13 tasks from 5 different benchmarks, while outperforming the models fine-tuned with state-of-the-art data synthesis methods like Evol-Instruct, DataTune and Prompt2Model.