Multipath transmission (MT) promotes transmission quality effectively. Path diversity (PD) impacts MT quality by aggregating capabilities of paths with little correlation. Enough PD contributes to improving concurrent link utilization and weakening negative impacts from a single path so that abilities of congestion and failure tolerance are enhanced. However, PD is hard to guarantee on overlay networks due to little awareness of underlay networks and few evaluation methods.In this paper, we propose the spatial geometry-based multipath routing (SGMR) method to improve PD for MT on overlay networks. Considering that paths are composed of overlay nodes and network coordinates effectively characterize node diversity (ND), we employ some geometric mechanisms on the spatial coordinate-based view to convert ND to PD. Firstly, coordinates are generated to match the overlay and underlay networks and meanwhile to characterize ND.Then, for generating multiple paths, transmission direction facilitates the path convergence, transmission surface constrains intermediate nodes, and deviation angle guarantees link diversity. Simulation and real-world evaluations demonstrate that SGMR guarantees PD better, and the multipath transmission quality is improved thanks to enough PD.