  In nature, the process of cellular growth and differentiation has lead to an
amazing diversity of organisms -- algae, starfish, giant sequoia, tardigrades,
and orcas are all created by the same generative process. Inspired by the
incredible diversity of this biological generative process, we propose a
generative model, the Variational Neural Cellular Automata (VNCA), which is
loosely inspired by the biological processes of cellular growth and
differentiation. Unlike previous related works, the VNCA is a proper
probabilistic generative model, and we evaluate it according to best practices.
We find that the VNCA learns to reconstruct samples well and that despite its
relatively few parameters and simple local-only communication, the VNCA can
learn to generate a large variety of output from information encoded in a
common vector format. While there is a significant gap to the current
state-of-the-art in terms of generative modeling performance, we show that the
VNCA can learn a purely self-organizing generative process of data.
Additionally, we show that the VNCA can learn a distribution of stable
attractors that can recover from significant damage.
