Speculative decoding accelerates large language model (LLM) inference by allowing a lightweight draft model to propose candidate tokens for verification by a target model. In real-world deployments, however, shifts in input distributions and updates to the target model can weaken draft–target alignment, reducing token acceptance and acceleration. Repeatedly retraining the draft model is costly, delays deployment, and may impair performance on previously encountered distributions. Achieving online alignment therefore requires rapid and stable adaptation while incorporating real-time feedback within a limited compute budget. To this end, we propose Dynamic Speculative Decoding (DySD), a framework that aligns the draft model with the target model during inference without offline retraining. DySD combines hierarchical feature alignment with distribution-level matching and uses divergence-triggered dynamic distillation to selectively update the draft model. Experiments across multiple datasets show that DySD achieves 1.6×–2.0× speedups and boosts token acceptance rates by 10%–30% under distribution shifts, enabling speculative decoding to remain fast, stable, and adaptive in ever-changing environments.