Building on recent advances in video generation, generative video compression has emerged as a new paradigm for achieving visually pleasing reconstructions. However, existing methods exhibit limited exploitation of temporal correlations, causing noticeable flicker and degraded temporal coherence at ultra-low bitrates. In this paper, we propose Free-GVC, a training-free generative video compression framework that reformulates video coding as latent trajectory compression guided by a video diffusion prior. Our method operates at the group-of-pictures (GOP) level, encoding video segments into a compact latent space and progressively compressing them along the diffusion trajectory. To ensure perceptually consistent reconstruction across GOPs, we introduce an Adaptive Quality Control module that dynamically constructs an online rate-perception surrogate model to predict the optimal diffusion step for each GOP. In addition, an Inter-GOP Alignment module establishes frame overlap and performs latent fusion between adjacent groups, thereby mitigating flicker and enhancing temporal coherence. Experiments show that Free-GVC achieves an average of 93.29% BD-Rate reduction in DISTS over the latest neural codec DCVC-RT, and a user study further confirms its superior perceptual quality and temporal coherence at ultra-low bitrates.