We aim to develop a model-based planning framework for world models that can be scaled with increasing model and data budgets for general-purpose manipulation tasks with only language and vision inputs. To this end, we present FLow-CentrIc generative Planning (FLIP), a model-based planning algorithm on visual space that features three key modules: 1) a multi-modal flow generation model as the general-purpose action proposal module; 2) a flow-conditioned video generation model as the dynamics module; and 3) a vision-language representation learning model as the value module. Given an initial image and language instruction as the goal, FLIP can progressively search for long-horizon flow and video plans that maximize the discounted return to accomplish the task. FLIP is able to synthesize long-horizon plans across objects, robots, and tasks with image flows as the general action representation, and the dense flow information also provides rich guidance for long-horizon video generation. In addition, the synthesized flow and video plans can guide the training of low-level control policies for robot execution. Experiments on diverse benchmarks demonstrate that FLIP can improve both the success rates and quality of long-horizon video plan synthesis and has the interactive world model property, opening up wider applications for future works. Video demos are on our website: https://nus-lins-lab.github.io/flipweb/.

Dexterous grasping is a fundamental yet challenging skill in robotic manipulation, requiring precise interaction between robotic hands and objects. In this paper, we present$\mathcal{D}(\mathcal{R}, \mathcal{O})$Grasp, a novel framework that models the interaction between the robotic hand in its grasping pose and the object, enabling broad generalization across various robot hands and object geometries. Our model takes the robot hand's description and object point cloud as inputs and efficiently predicts kinematically valid and stable grasps, demonstrating strong adaptability to diverse robot embodiments and object geometries. Extensive experiments conducted in both simulated and real-world environments validate the effectiveness of our approach, with significant improvements in success rate, grasp diversity, and inference speed across multiple robotic hands. Our method achieves an average success rate of$87.53\%$in simulation in less than one second, tested across three different dexterous robotic hands. In real-world experiments using the LeapHand, the method also demonstrates an average success rate of$\mathbf{8 9\%}. \mathcal{D}(\mathcal{R}, \mathcal{O})$Grasp provides a robust solution for dexterous grasping in complex and varied environments. The code, appendix, and videos are available on our project website at https://nus-lins-lab.github.io/drograspweb/.