# Particle Flow Bayes' Rule

arXiv: https://arxiv.org/abs/1902.00640 · HTML: https://mlsanity.com/paper/1902.00640/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Feb 2019.

## Built on by (most cited first, 5 of 5)

- [RNN with Particle Flow for Probabilistic Spatio-temporal Forecasting](https://mlsanity.com/paper/2106.06064/) (2021)
- [Hierarchical Neural Simulation-Based Inference Over Event Ensembles](https://mlsanity.com/paper/2306.12584/) (2023)
- [Learning Energy-Based Generative Models via Potential Flow: A Variational Principle Approach to Probability Density Homotopy Matching](https://mlsanity.com/paper/2504.16262/) (2025)
- [Physics-informed neural particle flow for the Bayesian update step](https://mlsanity.com/paper/2602.23089/) (2026)
- [Variational Potential Flow: A Novel Probabilistic Framework for Energy-Based Generative Modelling](https://mlsanity.com/paper/2407.15238/) (2024)

## Abstract (arXiv)

We present a particle flow realization of Bayes' rule, where an ODE-based neural operator is used to transport particles from a prior to its posterior after a new observation. We prove that such an ODE operator exists. Its neural parameterization can be trained in a meta-learning framework, allowing this operator to reason about the effect of an individual observation on the posterior, and thus generalize across different priors, observations and to sequential Bayesian inference. We demonstrated the generalization ability of our particle flow Bayes operator in several canonical and high dimensional examples.