Unsupervised point cloud completion aims to infer the whole geometry of a partial object observation without requiring partial-complete correspondence. Differing from existing deterministic approaches, we advocate generative modeling based unsupervised point cloud completion to explore the missing correspondence. Specifically, we propose a novel framework that performs completion by transforming a partial shape encoding into a complete one using a latent transport module, and it is designed as a latent-space energy-based model (EBM) in an encoder-decoder architecture, aiming to learn a probability distribution conditioned on the partial shape encoding. To train the latent code transport module and the encoder-decoder network jointly, we introduce a residual sampling strategy, where the residual captures the domain gap between partial and complete shape latent spaces. As a generative model-based framework, our method can produce uncertainty maps consistent with human perception, leading to explainable unsupervised point cloud completion. We experimentally show that the proposed method produces high-fidelity completion results, outperforming state-of-the-art models by a significant margin.