# Variational Neural Cellular Automata

arXiv: https://arxiv.org/abs/2201.12360 · HTML: https://mlsanity.com/paper/2201.12360/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2022.

## Built on by (most cited first, 28 of 28)

- [Attention-based Neural Cellular Automata](https://mlsanity.com/paper/2211.01233/) (2022)
- [Med-NCA: Robust and Lightweight Segmentation with Neural Cellular Automata](https://mlsanity.com/paper/2302.03473/) (2023)
- [Neural Cellular Automata for ARC-AGI](https://mlsanity.com/paper/2506.15746/) (2025)
- [Goal-Guided Neural Cellular Automata: Learning to Control Self-Organising Systems](https://mlsanity.com/paper/2205.06806/) (2022)
- [E(n)-equivariant Graph Neural Cellular Automata](https://mlsanity.com/paper/2301.10497/) (2023)
- [Frequency-Time Diffusion with Neural Cellular Automata](https://mlsanity.com/paper/2401.06291/) (2024)
- [Neural cellular automata: applications to biology and beyond classical AI](https://mlsanity.com/paper/2509.11131/) (2025)
- [CAX: Cellular Automata Accelerated in JAX](https://mlsanity.com/paper/2410.02651/) (2024)
- [NoiseNCA: Noisy Seed Improves Spatio-Temporal Continuity of Neural Cellular Automata](https://mlsanity.com/paper/2404.06279/) (2024)
- [EngramNCA: a Neural Cellular Automaton Model of Memory Transfer](https://mlsanity.com/paper/2504.11855/) (2025)
- [Learning Locally Interacting Discrete Dynamical Systems: Towards Data-Efficient and Scalable Prediction](https://mlsanity.com/paper/2404.06460/) (2024)
- [Neural Cellular Automata: From Cells to Pixels](https://mlsanity.com/paper/2506.22899/) (2025)
- [AdaNCA: Neural Cellular Automata As Adaptors For More Robust Vision Transformer](https://mlsanity.com/paper/2406.08298/) (2024)
- [An Organism Starts with a Single Pix-Cell: A Neural Cellular Diffusion for High-Resolution Image Synthesis](https://mlsanity.com/paper/2407.03018/) (2024)
- [A New Kind of Network? Review and Reference Implementation of Neural Cellular Automata](https://mlsanity.com/paper/2604.24990/) (2026)
- [MedSegDiffNCA: Diffusion Models With Neural Cellular Automata for Skin Lesion Segmentation](https://mlsanity.com/paper/2501.02447/) (2025)
- [rNCA: Self-Repairing Segmentation Masks](https://mlsanity.com/paper/2512.13397/) (2025)
- [Remapping and navigation of an embedding space via error minimization: a fundamental organizational principle of cognition in natural and artificial systems](https://mlsanity.com/paper/2601.14096/) (2026)
- [Coarse to Fine: Iterative Adversarial Neural Cellular Automata for Medical Image Synthesis](https://mlsanity.com/paper/2608.28909/) (2026)
- [Neural Cellular Automata Learn General Features in their Hidden Channels](https://mlsanity.com/paper/2609.21870/) (2026)
- [Mixtures of Neural Cellular Automata: A Stochastic Framework for Growth Modelling and Self-Organization](https://mlsanity.com/paper/2506.20486/) (2025)
- [Missing Data Imputation using Neural Cellular Automata](https://mlsanity.com/paper/2509.00651/) (2025)
- [Conditional Morphogenesis: Emergent Generation of Structural Digits via Neural Cellular Automata](https://mlsanity.com/paper/2512.08360/) (2025)
- [DiffeoMorph: Learning to Morph 3D Shapes Using Differentiable Agent-Based Simulations](https://mlsanity.com/paper/2512.17129/) (2025)
- [Learning PDE Time-Stepping with Neural Cellular Automata](https://mlsanity.com/paper/2608.30328/) (2026)
- [Applications of Neural Cellular Automata: State of the Art, Challenges and Opportunities](https://mlsanity.com/paper/2609.24595/) (2026)
- [Where Does Randomness Matter in Neural Cellular Automata?](https://mlsanity.com/paper/2609.36797/) (2026)
- [2D Spatial Reasoning with Adaptive Neural Cellular Automata](https://mlsanity.com/paper/2610.08518/) (2026)

## Abstract (arXiv)

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.