# Progressive Bayesian Particle Flows based on Optimal Transport Map Sequences

arXiv: https://arxiv.org/abs/2303.02412 · HTML: https://mlsanity.com/paper/2303.02412/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 4 Mar 2023.

## Builds on (most cited first, 8 of 8)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Coupling techniques for nonlinear ensemble filtering](https://mlsanity.com/paper/1907.00389/) (2019)
- [Inference via low-dimensional couplings](https://mlsanity.com/paper/1703.06131/) (2017)
- [Optimal Reduction of Multivariate Dirac Mixture Densities](https://mlsanity.com/paper/1411.4586/) (2014)
- [The Smart Sampling Kalman Filter with Symmetric Samples](https://mlsanity.com/paper/1506.03254/) (2015)
- [Stochastic Particle Flow for Nonlinear High-Dimensional Filtering Problems](https://mlsanity.com/paper/1511.01448/) (2015)
- [FLUX: Progressive State Estimation Based on Zakai-type Distributed Ordinary Differential Equations](https://mlsanity.com/paper/1808.02825/) (2018)

## Built on by (most cited first, 1 of 1)

- [Newton-Flow Particle Filters based on Generalized Cram'er Distance](https://mlsanity.com/paper/2509.00182/) (2025)

## Abstract (arXiv)

We propose a method for optimal Bayesian filtering with deterministic particles. In order to avoid particle degeneration, the filter step is not performed at once. Instead, the particles progressively flow from prior to posterior. This is achieved by splitting the filter step into a series of sub-steps. In each sub-step, optimal resampling is done by a map that replaces non-equally weighted particles with equally weighted ones. Inversions of the maps or monotonicity constraints are not required, greatly simplifying the procedure. The parameters of the mapping network are optimized w.r.t. to a particle set distance. This distance is differentiable, and compares non-equally and equally weighted particles. Composition of the map sequence provides a final mapping from prior to posterior particles. Radial basis function neural networks are used as maps. It is important that no intermediate continuous density representation is required. The entire flow works directly with particle representations. This avoids costly density estimation.