# An overview of differentiable particle filters for data-adaptive sequential Bayesian inference

arXiv: https://arxiv.org/abs/2302.09639 · HTML: https://mlsanity.com/paper/2302.09639/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 109 references that are in the map.
- First posted on arXiv 19 Feb 2023.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Variational Sequential Monte Carlo](https://mlsanity.com/paper/1705.11140/) (2017)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [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)
- [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)
- [Multimodal Sensor Fusion with Differentiable Filters](https://mlsanity.com/paper/2010.13021/) (2020)
- [Discriminative Particle Filter Reinforcement Learning for Complex Partial Observations](https://mlsanity.com/paper/2002.09884/) (2020)
- [Differentiable Algorithm Networks for Composable Robot Learning](https://mlsanity.com/paper/1905.11602/) (2019)
- [How to Train Your Differentiable Filter](https://mlsanity.com/paper/2012.14313/) (2020)
- [Particle Gibbs with Ancestor Sampling](https://mlsanity.com/paper/1401.0604/) (2014)
- [Towards Differentiable Resampling](https://mlsanity.com/paper/2004.11938/) (2020)
- [Differentiable Particle Filters through Conditional Normalizing Flow](https://mlsanity.com/paper/2107.00488/) (2021)
- [End-To-End Semi-supervised Learning for Differentiable Particle Filters](https://mlsanity.com/paper/2011.05748/) (2020)
- [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)

## Built on by (most cited first, 23 of 23)

- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [Exact nonlinear state estimation](https://mlsanity.com/paper/2310.10976/) (2023)
- [Enhanced SMC2: Leveraging Gradient Information from Differentiable Particle Filters Within Langevin Proposals](https://mlsanity.com/paper/2407.17296/) (2024)
- [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)
- [Regime Learning for Differentiable Particle Filters](https://mlsanity.com/paper/2405.04865/) (2024)
- [Deep Variational Sequential Monte Carlo for High-Dimensional Observations](https://mlsanity.com/paper/2501.05982/) (2025)
- [DiffPF: Differentiable Particle Filtering with Generative Sampling via Conditional Diffusion Models](https://mlsanity.com/paper/2507.15716/) (2025)
- [PyDPF: A Python Package for Differentiable Particle Filtering](https://mlsanity.com/paper/2510.25693/) (2025)
- [Diffusion differentiable resampling](https://mlsanity.com/paper/2512.10401/) (2025)
- [Hess-MC2: Sequential Monte Carlo Squared using Hessian Information and Second Order Proposals](https://mlsanity.com/paper/2507.07461/) (2025)
- [Sequential Bayesian Design for Efficient Surrogate Construction in the Inversion of Darcy Flows](https://mlsanity.com/paper/2507.17713/) (2025)
- [Auto-differentiable data assimilation: Co-learning of states, dynamics, and filtering algorithms](https://mlsanity.com/paper/2603.20891/) (2026)
- [Differentiable Particle Filtering using Optimal Placement Resampling](https://mlsanity.com/paper/2402.16639/) (2024)
- [The Artificial Neural Twin -- Process Optimization and Continual Learning in Distributed Process Chains](https://mlsanity.com/paper/2403.18343/) (2024)
- [Towards Interpretable Visuo-Tactile Predictive Models for Soft Robot Interactions](https://mlsanity.com/paper/2407.12197/) (2024)
- [Inverse Particle Filter](https://mlsanity.com/paper/2407.16623/) (2024)
- [Learning state and proposal dynamics in state-space models using differentiable particle filters and neural networks](https://mlsanity.com/paper/2411.15638/) (2024)
- [pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements](https://mlsanity.com/paper/2510.27503/) (2025)
- [VSE: Variational state estimation of complex model-free process](https://mlsanity.com/paper/2601.21887/) (2026)
- [DNS: Data-driven Nonlinear Smoother for Complex Model-free Process](https://mlsanity.com/paper/2602.08560/) (2026)
- [Efficient Learning of Deep State Space Models via Importance Smoothing](https://mlsanity.com/paper/2605.21108/) (2026)
- [Generative Model Proposal based Particle Filtering for Data Assimilation](https://mlsanity.com/paper/2607.01012/) (2026)

## Abstract (arXiv)

By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been recognised in various applications, their performance relies on the knowledge of dynamic models and measurement models, as well as the construction of effective proposal distributions. An emerging trend involves constructing components of particle filters using neural networks and optimising them by gradient descent, and such data-adaptive particle filtering approaches are often called differentiable particle filters. Due to the expressiveness of neural networks, differentiable particle filters are a promising computational tool for performing inference on sequential data in complex, high-dimensional tasks, such as vision-based robot localisation. In this paper, we review recent advances in differentiable particle filters and their applications. We place special emphasis on different design choices for key components of differentiable particle filters, including dynamic models, measurement models, proposal distributions, optimisation objectives, and differentiable resampling techniques.