Unlike autoregressive large language models (AR-LLMs), diffusion LLMs (dLLMs) generate text by iteratively denoising many tokens in parallel, offering a promising path to efficient inference. Existing serving frameworks, however, schedule dLLM requests with policies designed for AR models, namely first-come-first-served (FCFS) admission and prefill priority. We find that both policies are ill-suited to dLLMs, wasting much of their speed. FCFS ignores that a dLLM request's decoding cost is highly heterogeneous and unknown at arrival, causing severe head-of-line blocking. Prefill priority, widely used in AR-LLM serving to keep time-to-first-token low, sharply cuts dLLM efficiency, as rounds that run only prompts leave most of the batch idle. We present DWISE, a Denoising Workload-Informed Scheduling Engine for efficient dLLM serving. DWISE schedules requests by their remaining work, measured in a block-level unit shared by prefill and denoising, so both phases share a round. To predict the unknown denoising workload, DWISE combines a lightweight prompt-based predictor at admission with a single refinement from the first denoising round's hidden states, which capture model-specific information absent from the prompt and require no additional model execution. Implemented in SGLang and evaluated on five models from three dLLM families under bursty workloads, DWISE reduces mean end-to-end latency over SGLang by 5.4$\times$ on average and up to 14.9$\times$ while preserving task accuracy. The code will be released publicly.

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