Diffusion language models (DLMs) have emerged as a powerful non-autoregressive alternative to GPT-style sequential generation, but suffer from substantial computational overhead due to their iterative parallel denoising. Existing acceleration works cannot accurately detect semantically stabilized tokens and then skip computation, leading to sub-optimal speedup in practice. This paper presents the first systematic study of convergence dynamics in DLMs. Innovative observations include the misalignment between traditionally used scalar detection criterion and the semantic convergence, and the post-peak confidence score, that wastes denoising computation and degrades inference quality. To address these limitations, we propose Ada-DLM, a semantic-aware adaptive denoising framework that encodes the trajectory of scalar confidence scores into an evolution-aware feature vector and then clusters vectors proactively and adaptively identify semantically converged tokens. Furthermore, we incorporate system-level optimizations to maximize runtime efficiency. Experiments show that Ada-DLM consistently outperforms the SOTA competitor, achieving up to 2x speedup and 19% quality improvement. That offers a practical path toward efficient high-quality DLM deployment.