Authors: Yi Shi, Mengchen Xu, Shuaihang Yuan, Yi Fang Description: Deep learning models have achieved great success in supervised shape descriptor learning for 3D shape retrieval, classification, and correspondence. However, the unsupervised shape descriptor calculated via deep learning is less studied than that of supervised ones due to the design challenges of unsupervised neural network architecture. This paper proposes a novel probabilistic framework for the learning of unsupervised deep shape descriptors with point distribution learning. In our approach, we firstly associate each point with a Gaussian, and the point clouds are modeled as the distribution of the points. We then use deep neural networks (DNNs) to model a maximum likelihood estimation process that is traditionally solved with an iterative Expectation-Maximization (EM) process. Our key novelty is that training'' these DNNs with unsupervised self-correspondence L2 distance loss will elegantly reveal the statically significant deep shape descriptor representation for the distribution of the point clouds. We have conducted experiments over various 3D datasets. Qualitative and quantitative comparisons demonstrate that our proposed method achieves superior classification performance over existing unsupervised 3D shape descriptors. In addition, we verified the following attractive properties of our shape descriptor through experiments: multi-scale shape representation, robustness to shape rotation, and robustness to noise.