# Differentiable Particle Filters through Conditional Normalizing Flow

arXiv: https://arxiv.org/abs/2107.00488 · HTML: https://mlsanity.com/paper/2107.00488/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 1 Jul 2021.

## Builds on (most cited first, 15 of 15)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Noise Flow: Noise Modeling with Conditional Normalizing Flows](https://mlsanity.com/paper/1908.08453/) (2019)
- [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)
- [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)
- [Particle Filter Recurrent Neural Networks](https://mlsanity.com/paper/1905.12885/) (2019)
- [Differentiable SLAM-net: Learning Particle SLAM for Visual Navigation](https://mlsanity.com/paper/2105.07593/) (2021)
- [How to Train Your Differentiable Filter](https://mlsanity.com/paper/2012.14313/) (2020)
- [Differentiable Factor Graph Optimization for Learning Smoothers](https://mlsanity.com/paper/2105.08257/) (2021)
- [End-To-End Semi-supervised Learning for Differentiable Particle Filters](https://mlsanity.com/paper/2011.05748/) (2020)

## Built on by (most cited first, 15 of 15)

- [An overview of differentiable particle filters for data-adaptive sequential Bayesian inference](https://mlsanity.com/paper/2302.09639/) (2023)
- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filters](https://mlsanity.com/paper/2111.01409/) (2021)
- [Unsupervised Learning of Sampling Distributions for Particle Filters](https://mlsanity.com/paper/2302.01174/) (2023)
- [Conditional Measurement Density Estimation in Sequential Monte Carlo via Normalizing Flow](https://mlsanity.com/paper/2203.08617/) (2022)
- [Sparse Graphical Linear Dynamical Systems](https://mlsanity.com/paper/2307.03210/) (2023)
- [Exact nonlinear state estimation](https://mlsanity.com/paper/2310.10976/) (2023)
- [Steering Deep Non-Linear Spatially Selective Filters for Weakly Guided Extraction of Moving Speakers in Dynamic Scenarios](https://mlsanity.com/paper/2505.14517/) (2025)
- [Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems](https://mlsanity.com/paper/2502.16232/) (2025)
- [Differentiable Bootstrap Particle Filters for Regime-Switching Models](https://mlsanity.com/paper/2302.10319/) (2023)
- [Learning Differentiable Particle Filter on the Fly](https://mlsanity.com/paper/2312.05955/) (2023)
- [Revisiting semi-supervised training objectives for differentiable particle filters](https://mlsanity.com/paper/2405.01251/) (2024)
- [DnD Filter: Differentiable State Estimation for Dynamic Systems using Diffusion Models](https://mlsanity.com/paper/2503.01274/) (2025)
- [Inverse Particle Filter](https://mlsanity.com/paper/2407.16623/) (2024)
- [Learning Flock: Enhancing Sets of Particles for Multi~Sub-State Particle Filtering with Neural Augmentation](https://mlsanity.com/paper/2408.11348/) (2024)

## Abstract (arXiv)

Differentiable particle filters provide a flexible mechanism to adaptively train dynamic and measurement models by learning from observed data. However, most existing differentiable particle filters are within the bootstrap particle filtering framework and fail to incorporate the information from latest observations to construct better proposals. In this paper, we utilize conditional normalizing flows to construct proposal distributions for differentiable particle filters, enriching the distribution families that the proposal distributions can represent. In addition, normalizing flows are incorporated in the construction of the dynamic model, resulting in a more expressive dynamic model. We demonstrate the performance of the proposed conditional normalizing flow-based differentiable particle filters in a visual tracking task.