Video Large Language Models (Video-LLMs) excel in video understanding but suffer from high inference latency due to autoregressive generation. Speculative Decoding (SD) mitigates this by applying a draft-and-verify paradigm, yet existing methods are constrained by rigid exact-match rules, severely limiting the acceleration potential. To bridge this gap, we propose LVSpec, the first training-free loosely SD framework tailored for Video-LLMs. Grounded in the insight that generation is governed by sparse visual-relevant anchors (mandating strictness) amidst abundant visual-irrelevant fillers (permitting loose verification), LVSpec employs a lightweight visual-relevant token identification scheme to accurately pinpoint the former. To further maximize acceptance, we augment this with a position-shift tolerant mechanism that effectively salvages positionally mismatched but semantically equivalent tokens. Experiments demonstrate that LVSpec is high-fidelity and rapid: it preserves >99.8% of target performance while accelerating Qwen2.5-VL-32B by 2.70 × and LLaVA-OneVision-72B by 2.94 ×. Notably, it boosts the mean accepted length and speedup ratio by 136% and 35% compared to SOTA training-free SD methods for Video-LLMs. Code is provided in the submitted software.

Parallel Speculative Decoding (PSD) accelerates traditional Speculative Decoding (SD) by overlapping draft generation with verification. However, it remains hampered by two fundamental challenges: (1) a theoretical speedup ceiling dictated by the speed ratio between the draft and target models, and (2) high computational waste and pipeline stall due to mid-sequence token rejections of early errors. To address these limitations, we introduce Double (Double Retrieval Speculative Parallelism). By bridging the gap between SD and PSD, our framework resolves the Retrieval Precision-Efficiency Dilemma through a novel synchronous mechanism. Specifically, we enable the draft model to execute iterative retrieval speculations to break the theoretical speedup limits; to alleviate rejections without rollback, the target model performs authoritative retrieval to generate multi-token guidance. Double is entirely training-free and lossless. Extensive experiments demonstrate state-of-the-art speedup of 5.3× on LLaMA3.3-70B and 2.8× on Qwen3-32B, significantly outperforming the advanced method EAGLE-3 that requires extensive model training. Our code is available at https://github.com/Sylvan820/Double1.