Abstract In this paper, we propose a normal estimation method for unstructured 3D point clouds. This method, called Nesti-Net, builds on a new local point cloud representation which consists of multi-scale point statistics (MuPS), estimated on a local coarse Gaussian grid. This representation is a suitable input to a CNN architecture. The normals are estimated using a mixtureof-experts (MoE) architecture, which relies on a datadriven approach for selecting the optimal scale around each point and encourages sub-network specialization. Interesting insights into the network’s resource distribution are provided. The scale prediction significantly improves robustness to different noise levels, point density variations and different levels of detail. We achieve state-of-the-art results on a benchmark synthetic dataset and present qualitative results on real scanned scenes.