Sparse Matrix-Dense Matrix Multiplication (SpMM) is a fundamental kernel in graph neural networks and scientific computing, yet its optimization on Ascend NPUs remains largely unexplored. The physically decoupled Cube/Vector architecture and single-threaded scalar instruction dispatch of modern NPUs introduce unique challenges. We present Ascend-SpMM, a novel and systematic framework tailored to the physically decoupled architecture of Ascend NPUs.We introduce a memory-centric cost model that quantifies hardware affinity and guides a conflict-bounded, densityaware task-mapping strategy. The strategy maps dense regions to the high-throughput Cube path and sparse residuals to the flexible Vector path, with a theoretical bound on cross-processor conflicts. To execute these workloads with high efficiency, we further develop highly customized sub-kernels. These kernels leverage hierarchy-aware pipelining and round-robin ring buffer-based implicit synchronization to effectively mask memory latency and reduce instruction pipeline stalls. Extensive experiments demonstrate that Ascend-SpMM achieves a geometric-mean speedup of 12.70-20.55X over the strongest evaluated NPU baseline for each matrix, accelerates end-to-end GNN training by up to 6.8X, and delivers performance competitive with state-of-the-art GPU implementations. The source code of Ascend-SpMM is publicly available at https://github.com/IDMG-Lab/Ascend-SpMM.

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