Gradient perturbation mechanisms, such as differential privacy (DP), aim to defend against gradient inversion attacks (GIA) by injecting noise into the shared gradients. Recent studies have shown that DP-based defenses lack robustness against advanced GIAs. However, existing gradient inversion methods typically rely on iterative refinement and assume static noise, resulting in low efficiency and limited reconstruction fidelity under high-noise conditions. In this paper, we propose Venom, a novel gradient inversion attack method based on a liquid diffusion mechanism. Venom reconstructs private data directly from DP-protected gradients without requiring any prior knowledge of the noise distribution. Specifically, we design a Structural Prior Extraction (SPE) module that analytically extracts deep feature representations from perturbed gradients through energy-based aggregation, enabling stable pre-reconstruction of users' latent data features. We further introduce a Diffusion-driven Liquid Recovery Network (Diff-LRN) for high-fidelity image reconstruction. Unlike traditional diffusion models that rely on iterative sampling with predefined noise schedules, Diff-LRN performs deterministic single-step reconstruction using adaptive liquid neural dynamics to handle spatially heterogeneous noise patterns. Experiments across four benchmarks demonstrate that Venom achieves a speedup of up to 38,343× over state-of-the-art attacks while maintaining high reconstruction fidelity under strong DP settings. These results challenge prevailing assumptions about DP robustness and underscore the need for more resilient privacy-preserving mechanisms in federated learning.