Autoregressive Frontier Expansion: Growing Trees with Graph Machine Learning

Tree-like branching structures are common in nature, from botanical trees to neurons and respiratory trees. Their branching shape often reflects function, making structural modeling central to understanding how these systems work. Acquiring real-world 3D data via imaging can be expensive or infeasible, so realistic generative models are valuable for simulation and augmentation. Existing approaches either rely on hand-tuned, mechanistic procedures, or do not jointly generate both the tree topology and its 3D geometry. We propose a graph neural network architecture that generates trees through an iterative expansion process, simulating the biological growth of real trees. At each step, it grows the frontier by predicting whether each active branch should bifurcate or terminate. Experiments on botanical trees show that our method can learn the 3D branching structure across multiple trees.