In point cloud generation and completion, previous methods for transforming latent features to point clouds are generally based on fully connected layers (FC-based) or folding operations (Folding-based). However, point clouds generated by FC-based methods are usually troubled by outliers and rough surfaces. For folding-based methods, their data flow is large, convergence speed is slow, and they are also hard to handle the generation of non-smooth surfaces. In this work, we propose AXform, an attention-based method to transform latent features to point clouds. AXform first generates points in an interim space, using a fully connected layer. These interim points are then aggregated to generate the target point cloud. AXform takes both parameter sharing and data flow into account, which makes it has fewer outliers, fewer network parameters, and a faster convergence speed. The points generated by AXform do not have the strong 2-manifold constraint, which improves the generation of non-smooth surfaces. When AXform is expanded to multiple branches for local generations, the centripetal constraint makes it has properties of self-clustering and space consistency, which further enables unsupervised semantic segmentation. We also adopt this scheme and design AXformNet for point cloud completion. Considerable experiments on different datasets show that our methods achieve state-of-the-art results.