TreeSBM: Tree-Valued Schrödinger Bridges for Protein Evolution Forecasting

Protein evolution is a stochastic process in which ancestral sequences diversify into lineages that accumulate mutations and generate complex evolutionary trees. Existing protein language models, diffusion models, and flow-based generators forecast individual sequences, while phylogenetic methods reconstruct historical trees from observed descendants. The inverse problem, however, remains largely unexplored: *given a protein sequence, can we forecast the distribution of future evolutionary lineages that may emerge under selection pressures?* To answer this question, we introduce **Tree**-Valued **S**chrödinger **B**ridge **M**atching (**TreeSBM**), a generative framework for protein evolution forecasting. TreeSBM learns a tree-valued Schrödinger bridge between a reference evolutionary process and a distribution of observed evolutionary trees, transporting a root protein sequence into a distribution over future mutational histories. During inference, TreeSBM generates distributions of evolutionary trees forward in time conditioned on a single ancestral sequence, jointly modeling sequence evolution, lineage diversification, and branching topology. Across viral evolution forecasting benchmarks, TreeSBM supports realistic and high fitness evolutionary tree generation, strong future lineage forecasting, and probabilistic exploration of evolutionary spaces. On SARS-CoV-2 generated variants, TreeSBM recovers pandemic-grade threats and other observed high fitness mutations. These results establish tree-valued Schrödinger bridges as a framework for forecasting branching processes in protein evolution. For reproducibility, we host our code, data-processing scripts, and evaluation pipelines at this anonymous repository: [https://anonymous.4open.science/r/TreeSBM-D7EC](https://anonymous.4open.science/r/TreeSBM-D7EC).