Phylogenetic trees elucidate evolutionary relationships among species, but phylogenetic inference remains challenging due to the complexity of combining continuous (branch lengths) and discrete parameters (tree topology). Traditional Markov Chain Monte Carlo methods face slow convergence and computational burdens. Existing Variational Inference methods, which require pre-generated topologies and typically treat tree structures and branch lengths independently, may overlook critical sequence features, limiting their accuracy and flexibility. We propose PhyloGen, a novel method leveraging a pre-trained genomic language model to generate and optimize phylogenetic trees without dependence on evolutionary models or aligned sequence constraints. PhyloGen views phylogenetic inference as a conditionally constrained tree structure generation problem, jointly optimizing tree topology and branch lengths through three core modules: (i) Feature Extraction, (ii) PhyloTree Construction, and (iii) PhyloTree Structure Modeling. Meanwhile, we introduce a Scoring Function to guide the model towards a more stable gradient descent. We demonstrate the effectiveness and robustness of PhyloGen on eight real-world benchmark datasets. Visualization results confirm PhyloGen provides deeper insights into phylogenetic relationships.

Phylogenetic inference, grounded in molecular evolution models, is essential for understanding the evolutionary relationships in biological data. Accounting for the uncertainty of phylogenetic tree variables, which include tree topologies and evolutionary distances on branches, is crucial for accurately inferring species relationships from molecular data and tasks requiring variable marginalization. Variational Bayesian methods are key to developing scalable, practical models; however, it remains challenging to conduct phylogenetic inference without restricting the combinatorially vast number of possible tree topologies. In this work, we introduce a novel, fully differentiable formulation of phylogenetic inference that leverages a unique representation of topological distributions in continuous geometric spaces. Through practical considerations on design spaces and control variates for gradient estimations, our approach, GeoPhy, enables variational inference without limiting the topological candidates. In experiments using real benchmark datasets, GeoPhy significantly outperformed other approximate Bayesian methods that considered whole topologies.

Designing flexible probabilistic models over tree topologies is important for developing efficient phylogenetic inference methods. To do that, previous works often leverage the similarity of tree topologies via hand-engineered heuristic features which would require domain expertise and may suffer from limited approximation capability. In this paper, we propose a deep autoregressive model for phylogenetic inference based on graph neural networks (GNNs), called ARTree. By decomposing a tree topology into a sequence of leaf node addition operations and modeling the involved conditional distributions based on learnable topological features via GNNs, ARTree can provide a rich family of distributions over tree topologies that have simple sampling algorithms, without using heuristic features. We demonstrate the effectiveness and efficiency of our method on a benchmark of challenging real data tree topology density estimation and variational Bayesian phylogenetic inference problems.

We show that VBPI-NF significantly improves upon the vanilla VBPI on a benchmark of challenging real data Bayesian phylogenetic inference problems.