Discrete diffusion learns to sample phylogenetic trees

Ethan Baron, Alan N. Amin, and Andrew Gordon Wilson have introduced a conditional generative model that samples evolutionary tree topologies directly from sequence alignments. Their paper, accepted at NeurIPS 2026, applies discrete diffusion to tree structure and reports competitive results on synthetic data and standard Bayesian phylogenetics benchmarks.

The authors informally call the approach DeepPhylo. It shifts computation into simulation and neural-network training, allowing inference under evolutionary processes whose likelihoods are difficult or impractical to evaluate. Once trained, the model generates posterior samples through an iterative reverse process conditioned on an observed DNA or protein alignment.

Likelihoods set the ceiling

Phylogenetic inference estimates evolutionary relationships among taxa from their sequences. Bayesian workflows define a prior over trees and evolutionary parameters, evaluate the sequence likelihood for each candidate, and use Markov chain Monte Carlo, or MCMC, to approximate the resulting posterior distribution.

Standard substitution models can incorporate features such as unequal base frequencies and variation in mutation rates across sites. Their tractability still depends on simplifying assumptions, including limited dependence between positions and a fixed alignment. Jointly modeling substitutions, insertions, deletions, selection, and site-specific interactions can make likelihood evaluation prohibitively expensive.

Maximum-likelihood tools such as IQ-TREE offer fast, mature inference under a broad family of tractable models. Their estimates remain tied to the selected likelihood model, while MCMC adds the cost of exploring a vast space of possible topologies and parameters. For \(n\) labeled taxa, the number of binary tree topologies grows super-exponentially with \(n\).