Phylogenetic posteriors get an iterative generative model: it matches IQ-Tree on simple data and beats it on complex evolution
Synopsis
Posterior inference over phylogenetic trees has depended on likelihoods, which become intractable once real processes such as insertions, deletions or site selection are modeled. This family of conditional generative models builds a tree step by step, bottom-up, middle-out or top-down, and is trained with a discrete diffusion objective; on real and synthetic data it recovers MCMC posteriors more closely than the prior simulation-based method Phyloformer 2, matches IQ-Tree on simple data, and is reliably more accurate on more realistic complex models.
Interpretation
A generative model trained only on simulated data can now sample posteriors over phylogenetic trees directly, without writing down the likelihood of the evolutionary model. Bayesian inference has relied on MCMC, which needs a likelihood; for models with insertions and deletions, selection dependence between sites, or context-dependent mutation rates the likelihood is intractable, so practitioners settle for simplified models they know are misspecified or discard data. On eight classical real evolutionary datasets and synthetic data of matching size, the MMD distance between sampled trees and MrBayes gold-standard posteriors is much smaller than for the prior simulation-based method Phyloformer 2, near zero on synthetic data and larger on real data.
Rather than emitting a whole tree in one pass, the model runs many forward passes, each deciding which taxa to merge, graft or percolate next given the partial tree built so far. The prior simulation-based method Phyloformer 2 uses a single forward pass with fixed embeddings to parameterize the whole tree distribution, so a later merge probability cannot depend on earlier merges. All three construction paradigms are parameterized as graph neural networks and trained with a discrete diffusion objective for about 100 GPU hours; on DNA or protein sequence data, all three achieve better ELBOs than Phyloformer 2, with the bottom-up paradigm best on simple data.
Under complex evolutionary models with intractable likelihoods, the model's point-estimate trees are closer to the true tree than those from the widely used maximum-likelihood tool IQ-Tree. IQ-Tree is a reliable baseline when the simple model is correctly specified, but on data with protein site selection (CAT) and insertions and deletions (InDel) it ignores those effects. Measured by unrooted Robinson-Foulds distance to the true tree, the models match IQ-Tree on JC data and outperform IQ-Tree, and IQ-Tree Flex, on CAT and InDel data; the bottom-up and middle-out models also sample faster than IQ-Tree in most settings.
Perspective
The demonstrated scope is eight classical real datasets plus synthetic data of matching size, covering JC, CAT and InDel evolutionary models; the models infer tree topology only and do not predict branch lengths.
On real data the posteriors are under-confident, with posterior probabilities of high-probability splits systematically below MrBayes, and distributional distances on real data are clearly larger than on synthetic data; the authors list closing this gap and extending to branch lengths and species trees as future directions.