Diffusion Transformers (DiTs) have emerged as the state-of-the-art architecture for video generation, yet their computational and memory demands hinder practical deployment. While post-training quantization (PTQ) presents a promising approach to accelerate Video DiT models, existing methods suffer from two critical limitations: (1) dependence on computation-heavy and inflexible calibration procedures, and (2) considerable performance deterioration after quantization. To address these challenges, we propose DVD-Quant, a novel Data-free quantization framework for Video DiTs. Our approach integrates three key innovations: (1) Bounded-init Grid Refinement (BGR) and (2) Auto-scaling Rotated Quantization (ARQ) for calibration data-free quantization error reduction, as well as (3) $\delta$-Guided Bit Switching ($\delta$-GBS) for adaptive bit-width allocation. Extensive experiments across multiple video generation benchmarks demonstrate that DVD-Quant achieves an approximately 2$\times$ speedup over full-precision baselines on advanced DiT models while maintaining visual fidelity. Notably, DVD-Quant is the first to enable W4A4 PTQ for Video DiTs without compromising video quality. Code and models will be released to facilitate future research.