Rapid advancements in video diffusion models have enabled the creation of realistic videos, raising concerns about unauthorized use and driving the demand for techniques to protect model ownership. Existing watermarking methods suffer from two key limitations: they overlook temporal consistency due to conventional watermark decoders and degrade the visual quality of the generated videos. To address these issues, we introduce a robust watermarking method for latent video diffusion models named Latent Video Diffusion Watermarking (LVMark). We propose a novel watermark decoder tailored for generated videos by learning the consistency between adjacent frames. It ensures accurate message decoding, even under malicious attacks, by combining the low-frequency components of the three-dimensional wavelet domain with the color features of the video. Additionally, we train a latent decoder to maintain the visual fidelity of the generated video. Watermarks are embedded into layers with minimal impact on visual appearance using an importance-based weight modulation strategy. We optimize both the watermark decoder and the latent decoder of diffusion model, effectively balancing the trade-off between visual quality and bit accuracy. Our experiments show that our method embeds invisible watermarks into video diffusion models, ensuring robust decoding accuracy with 512-bit capacity, even under distortions.