Speculative decoding has emerged as a promising paradigm for accelerating large language model inference by leveraging a lightweight draft model to generate multiple candidate tokens. However, existing methods often incur substantial training overhead to mitigate information misalignment between autoregressive draft model training and decoding. To address this challenge, we propose EDSD, an Entropy-Driven Speculative Decoding framework that uses entropy as a unified, interpretable signal for both draft model training and architectural design. EDSD drives the draft model to progressively align with the target model in an easy-to-hard manner while establishing token-level alignment as a dominant design principle. Extensive experiments on seven LLMs demonstrate that EDSD improves training efficiency by 24.8%, increases the average acceptance length by 4.0%, and achieves a 4.1% speedup compared to state-of-the-art methods. Furthermore, EDSD improves robustness to system prompt variations by more than 5x. Our findings establish entropy-driven alignment as an effective and principled foundation for efficient speculative decoding.