TopoBox: towards Physically Feasible 3D Object Re-Arrangement via Topology-Aware Box Reasoning

3D object re-arrangement aims to discover vacant and well‑suited spaces for object movement and placement, which is an essential task in embodied interaction scenarios.While existing methods have effectively maintained **semantic consistency** with instructive conditions, they still show limitations on arranging spaces with **physical feasibility** (e.g., 3D dimension and orientation). Meanwhile, previous approaches ignore the **topological rationality** of the interaction between source objects and surrounding environments (e.g., structural support and collision-free connectivity), which also constrains the physical representation. To address these limitations, we propose **TopoBox**, a two-stage framework that leverages **Topo**logy-aware **Box** reasoning for physically feasible 3D object re-arrangement. At the first stage, we design a **Space Arrangement Predictor (Predictor)**, which explicitly localizes the 3D bounding box and concurrently forecasts an **interactive BoxSlot field**. At the second stage, we design a **Topological Box Reasoner (Reasoner)**, which utilizes the BoxSlot field as the core guidance, and realizes iterative topology refinement via multi-granularity and multi-surface feature sampling (i.e., box bottom, side, and upper surfaces). Furthermore, to address the lack of data for jointly modeling instruction-guided object rearrangement and its physical feasibility, we introduce ReArrange3D, a dataset comprising 78K+ instruction-guided re-arrangement instances, with comprehensive annotations to support modeling and evaluation. Extensive experiments conducted on **ReArrange3D** demonstrate that TopoBox surpasses State-Of-The-Art (SOTA) counterparts on placement accuracy and physical feasibility.