Video diffusion models can generate realistic and temporally consistent videos. This raises concerns about provenance, ownership, and integrity. Watermarking can help address these issues by embedding metadata directly into the content. To work well, a watermark needs enough capacity for meaningful metadata. It must also stay imperceptible and remain robust to common video manipulations. Existing methods struggle with limited capacity, extra inference cost, or reduced visual quality. We introduce VidStamp, a watermarking framework that embeds frame-level messages through the decoder of a latent video diffusion model. The decoder is fine-tuned in two stages. The first stage uses static image datasets to encourage spatial message separation. The second stage uses synthesized video sequences to restore temporal consistency. This approach enables high-capacity watermarks with minimal perceptual impact. VidStamp also supports dynamic watermarking through a control signal that selects message templates during inference. This adds flexibility and creates a second channel for communication. We evaluate VidStamp on Stable Video Diffusion (I2V), OpenSora, and Wan (T2V). The system embeds 48 bits per frame while preserving visual quality and staying robust to common distortions. Compared with VideoSeal, VideoShield, and RivaGAN, it achieves lower log P-values and stronger detectability. Its frame-wise watermarking design also enables precise temporal tamper localization, with an accuracy of 0.96, which exceeds the VideoShield baseline. Code: https://github.com/SPIN-UMass/VidStamp