# Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors

arXiv: https://arxiv.org/abs/1805.11122 · HTML: https://mlsanity.com/paper/1805.11122/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2018.

## Built on by (most cited first, 30 of 59)

- [Differentiable Particle Filtering via Entropy-Regularized Optimal Transport](https://mlsanity.com/paper/2102.07850/) (2021)
- [DiffStack: A Differentiable and Modular Control Stack for Autonomous Vehicles](https://mlsanity.com/paper/2212.06437/) (2022)
- [NeRF in detail: Learning to sample for view synthesis](https://mlsanity.com/paper/2106.05264/) (2021)
- [Differentiable SLAM-net: Learning Particle SLAM for Visual Navigation](https://mlsanity.com/paper/2105.07593/) (2021)
- [INVIGORATE: Interactive Visual Grounding and Grasping in Clutter](https://mlsanity.com/paper/2108.11092/) (2021)
- [Automatic Differentiation of Programs with Discrete Randomness](https://mlsanity.com/paper/2210.08572/) (2022)
- [Unbiased Asymmetric Reinforcement Learning under Partial Observability](https://mlsanity.com/paper/2105.11674/) (2021)
- [LASER: LAtent SpacE Rendering for 2D Visual Localization](https://mlsanity.com/paper/2204.00157/) (2022)
- [An overview of differentiable particle filters for data-adaptive sequential Bayesian inference](https://mlsanity.com/paper/2302.09639/) (2023)
- [Online Variational Filtering and Parameter Learning](https://mlsanity.com/paper/2110.13549/) (2021)
- [Differentiable Particle Filtering without Modifying the Forward Pass](https://mlsanity.com/paper/2106.10314/) (2021)
- [Differentiable Particle Filters through Conditional Normalizing Flow](https://mlsanity.com/paper/2107.00488/) (2021)
- [Deep Learning for Visual Localization and Mapping: A Survey](https://mlsanity.com/paper/2308.14039/) (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)
- [Compositional Learning-based Planning for Vision POMDPs](https://mlsanity.com/paper/2112.09456/) (2021)
- [Neural Extended Kalman Filters for Learning and Predicting Dynamics of Structural Systems](https://mlsanity.com/paper/2210.04165/) (2022)
- [Unsupervised Learning of Sampling Distributions for Particle Filters](https://mlsanity.com/paper/2302.01174/) (2023)
- [SIDE: State Inference for Partially Observable Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2105.06228/) (2021)
- [PILOT: Introducing Transformers for Probabilistic Sound Event Localization](https://mlsanity.com/paper/2106.03903/) (2021)
- [Variational Marginal Particle Filters](https://mlsanity.com/paper/2109.15134/) (2021)
- [Conditional Measurement Density Estimation in Sequential Monte Carlo via Normalizing Flow](https://mlsanity.com/paper/2203.08617/) (2022)
- [Learning Online Belief Prediction for Efficient POMDP Planning in Autonomous Driving](https://mlsanity.com/paper/2401.15315/) (2024)
- [Unrolling Particles: Unsupervised Learning of Sampling Distributions](https://mlsanity.com/paper/2110.02915/) (2021)
- [Streaming Motion Forecasting for Autonomous Driving](https://mlsanity.com/paper/2310.01351/) (2023)
- [Learning to be Smooth: An End-to-End Differentiable Particle Smoother](https://mlsanity.com/paper/2502.10546/) (2025)
- [Particle-Based Score Estimation for State Space Model Learning in Autonomous Driving](https://mlsanity.com/paper/2212.06968/) (2022)
- [Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems](https://mlsanity.com/paper/2502.16232/) (2025)
- [Learning Interpretable BEV Based VIO without Deep Neural Networks](https://mlsanity.com/paper/2109.12292/) (2021)
- [Learnable Spatio-Temporal Map Embeddings for Deep Inertial Localization](https://mlsanity.com/paper/2211.07635/) (2022)

## Abstract (arXiv)

We present differentiable particle filters (DPFs): a differentiable implementation of the particle filter algorithm with learnable motion and measurement models. Since DPFs are end-to-end differentiable, we can efficiently train their models by optimizing end-to-end state estimation performance, rather than proxy objectives such as model accuracy. DPFs encode the structure of recursive state estimation with prediction and measurement update that operate on a probability distribution over states. This structure represents an algorithmic prior that improves learning performance in state estimation problems while enabling explainability of the learned model. Our experiments on simulated and real data show substantial benefits from end-to- end learning with algorithmic priors, e.g. reducing error rates by ~80%. Our experiments also show that, unlike long short-term memory networks, DPFs learn localization in a policy-agnostic way and thus greatly improve generalization. Source code is available at https://github.com/tu-rbo/differentiable-particle-filters .