Visual imitation learning is effective for robots to learn versatile tasks. However, many existing methods rely on behavior cloning with supervised historical trajectories, limiting their 3D spatial and 4D spatiotemporal awareness. Consequently, these methods struggle to capture the 3D structures and 4D spatiotemporal relationships necessary for real-world deployment. In this work, we propose 4D Diffusion Policy (DP4), a novel visual imitation learning method that incorporates spatiotemporal awareness into diffusion-based policies. Unlike traditional approaches that rely on trajectory cloning, DP4 leverages a dynamic Gaussian world model to guide the learning of 3D spatial and 4D spatiotemporal perceptions from interactive environments. Our method constructs the current 3D scene from a single-view RGB-D observation and predicts the future 3D scene, optimizing trajectory generation by explicitly modeling both spatial and temporal dependencies. Extensive experiments across 17 simulation tasks with 173 variants and 3 real-world robotic tasks demonstrate that the 4D Diffusion Policy (DP4) outperforms baseline methods, improving the average simulation task success rate by 16.4% (Adroit), 14% (DexArt), and 6.45% (RLBench), and the average real-world robotic task success rate by 8.6%.

Performing language-conditioned robotic manipulation tasks in unstructured environments is highly demanded for general intelligent robots. Conventional robotic manipulation methods usually learn semantic representation of the observation for action prediction, which ignores the scene-level spatiotemporal dynamics for human goal completion. In this paper, we propose a dynamic Gaussian Splatting method named ManiGaussian for multi-task robotic manipulation, which mines scene dynamics via future scene reconstruction. Specifically, we first formulate the dynamic Gaussian Splatting framework that infers the semantics propagation in the Gaussian embedding space, where the semantic representation is leveraged to predict the optimal robot action. Then, we build a Gaussian world model to parameterize the distribution in our dynamic Gaussian Splatting framework, which provides informative supervision in the interactive environment via future scene reconstruction. We evaluate our ManiGaussian on 10 RLBench tasks with 166 variations, and the results demonstrate our framework can outperform the state-of-the-art methods by 13.1\% in average success rate.