Unfold The World: Factorize 4D Properties in Reinforcing Spatial Understanding

Despite the remarkable prowess of Vision-Language Models(VLMs) in general multimodal tasks, they remain fundamentally “flat”when reasoning about the physical world. We argue that this spatialbottleneck stems from a profound dimensional mismatch: while VLMsare trained to interpret 2D projections, true spatial reasoning demandsthe recovery of latent 3D geometry and temporal continuity. To conquerthis high-dimensional complexity, we advocate a shift from monolithiclearning to a “divide and conquer” paradigm. We present FactoSR, afactorized reinforcement learning framework that explicitly interpret the* Equal Contribution, † Project Lead, B Corresponding Authordimensions collapsed by visual projection. At its core, FactoSR decom-poses the monolithic problem of world-consistent reasoning into three or-thogonal, geometric sub-objectives: planar correspondence (XY ), depthconsistency (Z), and temporal reversibility (T ). By optimizing these ver-ifiable constraints within a unified policy learning mechanism, we effec-tively transform an ill-posed projection recovery problem into a series oftangible reasoning steps. Extensive evaluations on multi-view and videobenchmarks demonstrate that this elegant decomposition yields substan-tial gains in 3D and 4D reasoning, achieving a 5.9% boost on VSI-Benchand 4.5% on All-Angles-Bench. Our findings suggest that reinforcing ex-plicit, factorized 4D consistency is a critical step toward evolving VLMsinto robust, world-aware reasoners.Code: https://github.com/scott-yjyang/FactoSR