Autoregressive Frontier Expansion: Growing Trees with Graph Machine Learning

Umer Gupta, Saku Peltonen, Martin Ritzert

Track: tiny paper (up to 4 pages)

Keywords: tree, graph generation, iterative expansion, graph neural network, persistent homology

TL;DR: We trained a diffusion-based GNN generative model that grows realistic 3D tree structures by iteratively expanding and branching.

Abstract: 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.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Submission Number: 44