  We propose a probabilistic shape completion method extended to the continuous
geometry of large-scale 3D scenes. Real-world scans of 3D scenes suffer from a
considerable amount of missing data cluttered with unsegmented objects. The
problem of shape completion is inherently ill-posed, and high-quality result
requires scalable solutions that consider multiple possible outcomes. We employ
the Generative Cellular Automata that learns the multi-modal distribution and
transform the formulation to process large-scale continuous geometry. The local
continuous shape is incrementally generated as a sparse voxel embedding, which
contains the latent code for each occupied cell. We formally derive that our
training objective for the sparse voxel embedding maximizes the variational
lower bound of the complete shape distribution and therefore our progressive
generation constitutes a valid generative model. Experiments show that our
model successfully generates diverse plausible scenes faithful to the input,
especially when the input suffers from a significant amount of missing data. We
also demonstrate that our approach outperforms deterministic models even in
less ambiguous cases with a small amount of missing data, which infers that
probabilistic formulation is crucial for high-quality geometry completion on
input scans exhibiting any levels of completeness.
