While video compression based on implicit neural representations (INRs) has recently demonstrated great potential, existing INR-based video codecs still cannot achieve state-of-the-art (SOTA) performance compared to their conventional or autoencoder-based counterparts given the same coding configuration. In this context, we propose a Generative Implicit Video Compression framework, GIViC, aiming at advancing the performance limits of this type of coding methods. GIViC draws inspiration from the remarkable ability of large language and diffusion models to capture long-range dependencies, a characteristic also inherent to Implicit Neural Representations (INRs). Through the newly designed implicit diffusion process, GIViC performs diffusive sampling across coarse-to-fine spatiotemporal decompositions, gradually progressing from coarsergrained full-sequence diffusion to finer-grained per-token diffusion. A novel Hierarchical Gated Linear Attention-based transformer (HGLA), is also integrated into the framework, which dual-factorizes global dependency modeling along scale and sequential axes. The proposed GIViC model has been benchmarked against SOTA conventional and neural codecs using a Random Access (RA) configuration (YUV 4:2:0, GOPSize=32), and yields BD-rate savings of $15.94 \%, 22.46 \%$ and 8.52 % over VVC VTM, DCVC-FM and NVRC, respectively, on the UVG test set. As far as we are aware, GIViC is the first INR-based video codec that outperforms VTM, in terms of coding performance, based on the RA coding configuration.