Discrete diffusion language models (dLLMs) offer an attractive alternative to autoregressive generation by updating multiple tokens in parallel, but their inference efficiency is still limited by the cost of safely committing tentative predictions. In particular, speculative decoding for dLLMs is challenging because speculative tokens within the same diffusion block may depend on one another, making aggressive acceptance prone to error propagation and strict verification computationally expensive. We present PV-Decoding, a confidence-driven speculative decoding framework with progressive verification for block diffusion inference. PV-Decoding partitions masked positions into directly decoded tokens, speculative tokens, and unresolved tokens using two confidence thresholds, and then verifies speculative tokens with progressively stronger policies, including single-batch, dual-batch, and multi-batch verification. This design exposes a practical accuracy–efficiency trade-off: weaker verification minimizes overhead, whereas stronger verification improves acceptance precision and robustness. Experiments on three diffusion language models across GSM8K, MBPP, and HumanEval show that PV-Decoding reduces sequential model forward passes (MFPs) by 8%–37% relative to confidence-based decoding, while keeping the largest observed accuracy drop to 1.3%. On Dream-7B-Instruct/GSM8K, PV-Decoding (1-batch) and PV-Decoding (2-batch) improve throughput by 7.0%–13.6% under the same hardware budget, whereas PV-Decoding (multi-batch) is slower under the current runtime. These results suggest that confidence-guided speculation with structured verification is a practical path toward efficient and reliable dLLM inference.

Judge Decoding accelerates LLM inference by relaxing the strict verification of Speculative Decoding, yet it typically relies on expensive and noisy supervision. In this work, we revisit this paradigm from first principles, revealing that the “criticality” scores learned via costly supervision are intrinsically encoded in the draft-target distributional divergence. We theoretically prove a structural correspondence between learned linear judges and Kullback-Leibler (KL) divergence, demonstrating they rely on the same underlying logit primitives. Guided by this, we propose a simple, training-free verification mechanism based on KL divergence. Extensive experiments across reasoning and coding benchmarks show that our method matches or outperforms complex trained judges (e.g., AutoJudge), offering superior robustness to domain shifts and eliminating the supervision bottleneck entirely. Code is available at https://github.com/sunshy-1/JuDi.

Large Language Models (LLMs) have demonstrated impressive capabilities in natural language processing tasks, such as text generation and semantic understanding. However, their performance on numerical reasoning tasks, such as basic arithmetic, numerical retrieval, and magnitude comparison, remains surprisingly poor. This gap arises from their reliance on surface-level statistical patterns rather than understanding numbers as continuous magnitudes. Existing benchmarks primarily focus on either linguistic competence or structured mathematical problem-solving, neglecting fundamental numerical reasoning required in real-world scenarios. To bridge this gap, we propose NumericBench, a comprehensive benchmark to evaluate six fundamental numerical capabilities: number recognition, arithmetic operations, contextual retrieval, comparison, summary, and multi-step reasoning. NumericBench includes datasets ranging from synthetic number lists to crawled real-world data, addressing challenges like long contexts, noise, and multi-step reasoning. Extensive experiments on state-of-the-art LLMs, including GPT-4 and DeepSeek, reveal persistent weaknesses in numerical reasoning, highlighting the urgent need to improve numerically-aware language modeling. The benchmark is released in: https://github.com/TreeAI-Lab/NumericBench.