# Normalizing Flow-based Differentiable Particle Filters

arXiv: https://arxiv.org/abs/2403.01499 · HTML: https://mlsanity.com/paper/2403.01499/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 94 references that are in the map.
- First posted on arXiv 3 Mar 2024.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [DeepMind Lab](https://mlsanity.com/paper/1612.03801/) (2016)
- [Auto-Encoding Sequential Monte Carlo](https://mlsanity.com/paper/1705.10306/) (2017)
- [Particle Filter Networks with Application to Visual Localization](https://mlsanity.com/paper/1805.08975/) (2018)
- [Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors](https://mlsanity.com/paper/1805.11122/) (2018)
- [Differentiable Particle Filtering via Entropy-Regularized Optimal Transport](https://mlsanity.com/paper/2102.07850/) (2021)
- [Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks](https://mlsanity.com/paper/1301.3853/) (2013)
- [On Particle Methods for Parameter Estimation in State-Space Models](https://mlsanity.com/paper/1412.8695/) (2014)
- [Backprop KF: Learning Discriminative Deterministic State Estimators](https://mlsanity.com/paper/1605.07148/) (2016)
- [Fair Normalizing Flows](https://mlsanity.com/paper/2106.05937/) (2021)
- [Structured Output Learning with Conditional Generative Flows](https://mlsanity.com/paper/1905.13288/) (2019)
- [Particle Filter Recurrent Neural Networks](https://mlsanity.com/paper/1905.12885/) (2019)
- [Discriminative Particle Filter Reinforcement Learning for Complex Partial Observations](https://mlsanity.com/paper/2002.09884/) (2020)
- [How to Train Your Differentiable Filter](https://mlsanity.com/paper/2012.14313/) (2020)
- [An overview of differentiable particle filters for data-adaptive sequential Bayesian inference](https://mlsanity.com/paper/2302.09639/) (2023)
- [Particle Gibbs with Ancestor Sampling](https://mlsanity.com/paper/1401.0604/) (2014)
- [Towards Differentiable Resampling](https://mlsanity.com/paper/2004.11938/) (2020)
- [Differentiable Particle Filtering without Modifying the Forward Pass](https://mlsanity.com/paper/2106.10314/) (2021)

## Built on by (most cited first, 10 of 10)

- [Regime Learning for Differentiable Particle Filters](https://mlsanity.com/paper/2405.04865/) (2024)
- [DiffPF: Differentiable Particle Filtering with Generative Sampling via Conditional Diffusion Models](https://mlsanity.com/paper/2507.15716/) (2025)
- [Neural Bayesian Filtering](https://mlsanity.com/paper/2510.03614/) (2025)
- [PyDPF: A Python Package for Differentiable Particle Filtering](https://mlsanity.com/paper/2510.25693/) (2025)
- [Accelerated Inference for Partially Observed Markov Processes using Automatic Differentiation](https://mlsanity.com/paper/2407.03085/) (2024)
- [Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimation](https://mlsanity.com/paper/2601.07013/) (2026)
- [Efficient Learning of Deep State Space Models via Importance Smoothing](https://mlsanity.com/paper/2605.21108/) (2026)
- [Diffusion-Driven State Space Models](https://mlsanity.com/paper/2606.21036/) (2026)
- [Hierarchical Variational Kalman Filtering](https://mlsanity.com/paper/2607.00877/) (2026)
- [Generative Model Proposal based Particle Filtering for Data Assimilation](https://mlsanity.com/paper/2607.01012/) (2026)

## Abstract (arXiv)

Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian state-space models in complex environments. Existing differentiable particle filters are mostly constructed with vanilla neural networks that do not allow density estimation. As a result, they are either restricted to a bootstrap particle filtering framework or employ predefined distribution families (e.g. Gaussian distributions), limiting their performance in more complex real-world scenarios. In this paper we present a differentiable particle filtering framework that uses (conditional) normalizing flows to build its dynamic model, proposal distribution, and measurement model. This not only enables valid probability densities but also allows the proposed method to adaptively learn these modules in a flexible way, without being restricted to predefined distribution families. We derive the theoretical properties of the proposed filters and evaluate the proposed normalizing flow-based differentiable particle filters' performance through a series of numerical experiments.