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3D object detection in point clouds is a core component for modern robotics and autonomous driving systems. A key challenge in 3D object detection comes from the inherent sparse nature of point occupancy within the 3D scene. In this paper, we propose Sparse Window Transformer (SWFormer ), a scalable and accurate model for 3D object detection, which can take full advantage of the sparsity of point clouds. Built upon the idea of window-based Transformers, SWFormer converts 3D points into sparse voxels and windows, and then processes these variable-length sparse windows efficiently using a bucketing scheme. In addition to self-attention within each spatial window, our SWFormer also captures cross-window correlation with multi-scale feature fusion and window shifting operations. To further address the unique challenge of detecting 3D objects accurately from sparse features, we propose a new voxel diffusion technique. Experimental results on the Waymo Open Dataset show our SWFormer achieves state-of-the-art 73.36 L2 mAPH on vehicle and pedestrian for 3D object detection on the official test set, outperforming all previous single-stage and two-stage models, while being much more efficient.