Recently, video diffusion models (VDMs) have demonstrated the capability to accurately predict future image sequences, exhibiting a good understanding of physical dynamics. Motivated by the strong visual prediction capabilities of VDMs, we hypothesize that they inherently possess visual representations that reflect the evolution of the physical world, which we term predictive visual representations. Building on this hypothesis, we propose the Video Prediction Policy (VPP), a generalist robotic policy conditioned on the predictive visual representations from Video diffusion models. To further enhance these representations, we incorporate diverse human or robotic manipulation datasets, employing unified video-generation training objectives. VPP consistently outperforms existing methods across two simulated and two real-world benchmarks. Notably, it achieves a 41.5% relative improvement in the Calvin ABC-D benchmark compared to the previous state-of-the-art and delivers a 31.6% increase in success rates for complex real-world dexterous manipulation tasks.