# Improved Variational Bayesian Phylogenetic Inference with Normalizing Flows

arXiv: https://arxiv.org/abs/2012.00459 · HTML: https://mlsanity.com/paper/2012.00459/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2020.

## Built on by (most cited first, 17 of 17)

- [Learnable Topological Features for Phylogenetic Inference via Graph Neural Networks](https://mlsanity.com/paper/2302.08840/) (2023)
- [Multiple Importance Sampling ELBO and Deep Ensembles of Variational Approximations](https://mlsanity.com/paper/2202.10951/) (2022)
- [Variational Combinatorial Sequential Monte Carlo Methods for Bayesian Phylogenetic Inference](https://mlsanity.com/paper/2106.00075/) (2021)
- [GeoPhy: Differentiable Phylogenetic Inference via Geometric Gradients of Tree Topologies](https://mlsanity.com/paper/2307.03675/) (2023)
- [VaiPhy: a Variational Inference Based Algorithm for Phylogeny](https://mlsanity.com/paper/2203.01121/) (2022)
- [A Variational Approach to Bayesian Phylogenetic Inference](https://mlsanity.com/paper/2204.07747/) (2022)
- [ARTree: A Deep Autoregressive Model for Phylogenetic Inference](https://mlsanity.com/paper/2310.09553/) (2023)
- [Improved Variational Bayesian Phylogenetic Inference using Mixtures](https://mlsanity.com/paper/2310.00941/) (2023)
- [Efficient Mixture Learning in Black-Box Variational Inference](https://mlsanity.com/paper/2406.07083/) (2024)
- [Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space](https://mlsanity.com/paper/2501.17965/) (2025)
- [PhyloGen: Language Model-Enhanced Phylogenetic Inference via Graph Structure Generation](https://mlsanity.com/paper/2412.18827/) (2024)
- [Variational Bayesian Phylogenetic Inference with Semi-implicit Branch Length Distributions](https://mlsanity.com/paper/2408.05058/) (2024)
- [EvoVGM: a Deep Variational Generative Model for Evolutionary Parameter Estimation](https://mlsanity.com/paper/2205.13034/) (2022)
- [Prior Density Learning in Variational Bayesian Phylogenetic Parameters Inference](https://mlsanity.com/paper/2302.02522/) (2023)
- [Improving Tree Probability Estimation with Stochastic Optimization and Variance Reduction](https://mlsanity.com/paper/2409.05282/) (2024)
- [Variational phylogenetic inference with products over bipartitions](https://mlsanity.com/paper/2502.15110/) (2025)
- [PhylaFlow: Hybrid Flow Matching in Billera-Holmes-Vogtmann Tree Space for Phylogenetic Inference](https://mlsanity.com/paper/2605.21859/) (2026)

## Abstract (arXiv)

Variational Bayesian phylogenetic inference (VBPI) provides a promising general variational framework for efficient estimation of phylogenetic posteriors. However, the current diagonal Lognormal branch length approximation would significantly restrict the quality of the approximating distributions. In this paper, we propose a new type of VBPI, VBPI-NF, as a first step to empower phylogenetic posterior estimation with deep learning techniques. By handling the non-Euclidean branch length space of phylogenetic models with carefully designed permutation equivariant transformations, VBPI-NF uses normalizing flows to provide a rich family of flexible branch length distributions that generalize across different tree topologies. We show that VBPI-NF significantly improves upon the vanilla VBPI on a benchmark of challenging real data Bayesian phylogenetic inference problems. Further investigation also reveals that the structured parameterization in those permutation equivariant transformations can provide additional amortization benefit.