Tree-Conditioned Edit Flows for Ancestral Sequence Reconstruction

Phylogenetic trees are hybrid objects: branch lengths vary continuously, while topologies change discretely through edge contractions and expansions. Billera-Holmes-Vogtmann (BHV) tree space provides a canonical geometry for this structure, representing each resolved topology as a Euclidean orthant and topological changes as motion across shared lower-dimensional boundaries. We introduce PhylaFlow, a hybrid flow-matching model that learns posterior-basin transport in BHV tree space. PhylaFlow is trained on BHV geodesic paths from random starting trees to short-run posterior samples, coupling continuous branch-length motion within orthants with learned boundary events and discrete topology transitions. We evaluate the learned geometry operationally: if the flow reaches posterior-relevant regions, finite-budget Bayesian refinement initialized from, or guided by, its terminal trees should recover posterior-supported topologies more efficiently. Across DS1-DS8 phylogenetic posterior benchmarks, PhylaFlow substantially reduces initial Tree-KL relative to classical initializers. After finite-budget MrBayes refinement, direct PhylaFlow improves early and intermediate topology-recovery trajectories on most datasets, while split-guided PhylaFlow-MCMC obtains the strongest hard-case results. The best PhylaFlow variant outperforms short-warmup on seven of eight datasets and PhyloGFN on five of eight under the same refinement budget. In a joint sequence-conditioned experiment, sequence embeddings steer posterior split recovery, although exact posterior topology recovery remains preliminary. These results show that hybrid flow matching can learn actionable transport in BHV tree space and provide a geometry-aware proposal mechanism for Bayesian phylogenetic inference.

Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains challenging: the high complexity of tree space poses a significant obstacle for the current combinatorial and probabilistic techniques. In this paper, we adopt the framework of generative flow networks (GFlowNets) to tackle two core problems in phylogenetics: parsimony-based and Bayesian phylogenetic inference. Because GFlowNets are well-suited for sampling complex combinatorial structures, they are a natural choice for exploring and sampling from the multimodal posterior distribution over tree topologies and evolutionary distances. We demonstrate that our amortized posterior sampler, PhyloGFN, produces diverse and high-quality evolutionary hypotheses on real benchmark datasets. PhyloGFN is competitive with prior works in marginal likelihood estimation and achieves a closer fit to the target distribution than state-of-the-art variational inference methods. Our code is available at https://github.com/zmy1116/phylogfn.

Designing functional biological sequences requires navigating vast discrete spaces under strict evolutionary and biophysical constraints. Discrete Flow Matching (DFM) offers a generative framework over such spaces, but existing approaches rely on biologically uninformative couplings and offer limited flexibility for variable-length sequence generation and fine-grained control. We propose a structured coupling that encodes domain-specific preferences among sequence elements, biasing the source distribution toward plausible regions without modifying the flow objective or training procedure. Building on this, we introduce a latent edit-based rate parameterization that models variable-length generation via edit operations conditioned on a shared global latent, akin to a latent variable model, while remaining tractable. We further introduce a latent classifier-free guidance mechanism that steers generation coherently in continuous latent space, along with Dirichlet-prior temperature scaling for test-time control over edit operations. Our method achieves state-of-the-art performance across diverse biological sequence tasks, including density estimation, unconditional and conditional DNA sequence generation, and peptide sequence generation.