Most existing point cloud completion methods suffered from discrete nature of point clouds and unstructured prediction of points in local regions, which makes it hard to reveal fine local geometric details. To resolve this issue, we propose SnowflakeNet with Snowflake Point Deconvolution (SPD) to generate the complete point clouds. SPD models the generation of complete point clouds as the snowflake-like growth of points, where the child points are progressively generated by splitting their parent points after each SPD. Our insight of revealing detailed geometry is to introduce skip-transformer in SPD to learn point splitting patterns which can fit local regions the best. Skip-transformer leverages attention mechanism to summarize the splitting patterns used in previous SPD layer to produce the splitting in current SPD layer. The locally compact and structured point clouds generated by SPD precisely reveal the structure characteristic of 3D shape in local patches, which enables us to predict highly detailed geometries. Moreover, since SPD is a general operation, which is not limited to completion, we further explore the applications of SPD on other generative tasks, including point cloud auto-encoding, generation, single image reconstruction and upsampling. Our experimental results outperform the state-of-the-art methods under widely used benchmarks.