Existing generative video compression methods use generative models only as post-hoc reconstruction modules atop conventional codecs. We propose \emph{Generative Video Codec} (GVC), a zero-shot framework that turns a pretrained video generative model into the codec itself: the transmitted bitstream directly specifies the generative decoding trajectory, with no retraining required. To enable this, we convert the deterministic rectified-flow ODE of modern video foundation models into an equivalent SDE at inference time, unlocking per-step stochastic injection points for codebook-driven compression. Building on this unified backbone, we instantiate three complementary conditioning strategies -- \emph{Image-to-Video} (I2V) with adaptive tail-frame atom allocation, \emph{Text-to-Video} (T2V) operating at near-zero side information as a pure generative prior, and \emph{First-Last-Frame-to-Video} (FLF2V) with boundary-sharing GOP chaining for dual-anchor temporal control. Together, these variants span a principled trade-off space between spatial fidelity, temporal coherence, and compression efficiency. Experiments on standard benchmarks show that GVC achieves high-quality reconstruction below 0.002\,bpp while supporting flexible bitrate control through a single hyperparameter.

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