  We present a probabilistic 3D generative model, named Generative Cellular
Automata, which is able to produce diverse and high quality shapes. We
formulate the shape generation process as sampling from the transition kernel
of a Markov chain, where the sampling chain eventually evolves to the full
shape of the learned distribution. The transition kernel employs the local
update rules of cellular automata, effectively reducing the search space in a
high-resolution 3D grid space by exploiting the connectivity and sparsity of 3D
shapes. Our progressive generation only focuses on the sparse set of occupied
voxels and their neighborhood, thus enabling the utilization of an expressive
sparse convolutional network. We propose an effective training scheme to obtain
the local homogeneous rule of generative cellular automata with sequences that
are slightly different from the sampling chain but converge to the full shapes
in the training data. Extensive experiments on probabilistic shape completion
and shape generation demonstrate that our method achieves competitive
performance against recent methods.
