Learning a precise robotic grasping policy is crucial for embodied agents operating in complex real-world manipulation tasks. Despite significant advancements, most models still struggle with accurate spatial positioning of objects to be grasped. We first show that this spatial generalization challenge stems primarily from the extensive data requirements for adequate spatial understanding. However, collecting such data with real robots is prohibitively expensive, and relying on simulation data often leads to visual generalization gaps upon deployment. To overcome these challenges, we then focus on state-based policy generalization and present \textbf{ManiBox}, a novel bounding-box-guided manipulation method built on a simulation-based teacher-student framework. The teacher policy efficiently generates scalable simulation data using bounding boxes, which are proven to uniquely determine the objects' spatial positions. The student policy then utilizes these low-dimensional spatial states to enable zero-shot transfer to real robots. Through comprehensive evaluations in simulated and real-world environments, ManiBox demonstrates a marked improvement in spatial grasping generalization and adaptability to diverse objects and backgrounds. Further, our empirical study into scaling laws for policy performance indicates that spatial volume generalization scales with data volume in a power law. For a certain level of spatial volume, the success rate of grasping empirically follows Michaelis-Menten kinetics relative to data volume, showing a saturation effect as data increases. Our videos and code are available in https://thkkk.github.io/manibox.
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