Foundation Model Guided Flow Matching on Tree Manifold for Differentiable Phylogenetics

Abstract

Phylogenetic inference aims to reconstruct evolutionary relationships among entities with phylogenetic trees. However, this task remains challenging due to the large combinatorial space of tree topologies and continuous branch lengths. Traditional statistical methods usually face trade-offs between accuracy and computational efficiency. Recent deep learning approaches improve efficiency but often rely on prealigning sequences and constrained topological spaces. In this thesis, we propose a generative framework for phylogenetic inference that combines foundation-model sequence embeddings with structured modeling of tree space. We first introduce PhylaDiff, a diffusion-based model that represents trees as tokenized graphs and jointly generates topology and branch lengths. While PhylaDiff achieves strong reconstruction, we show that non-differentiable decoding limits its ability to incorporate likelihood-based objectives. To address this, we develop PhylaFlow, a flow-matching model that formulates phylogenetic inference as a continuous transport problem in Billera–Holmes–Vogtmann (BHV) space. The model learns a vector field over tree space, enabling differentiable generation of both topology and branch lengths. Results show stable training, reduced Robinson–Foulds distance, and lower KL divergence to the reference posterior. Overall, this work reframes phylogenetic inference as continuous generative modeling in a geometric space. The proposed framework improves efficiency and provides a new approach for modeling distributions over evolutionary trees.