# DnD Filter: Differentiable State Estimation for Dynamic Systems using Diffusion Models

arXiv: https://arxiv.org/abs/2503.01274 · HTML: https://mlsanity.com/paper/2503.01274/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 28 of its 45 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [ViNT: A Foundation Model for Visual Navigation](https://mlsanity.com/paper/2306.14846/) (2023)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [AdaptDiffuser: Diffusion Models as Adaptive Self-evolving Planners](https://mlsanity.com/paper/2302.01877/) (2023)
- [Diffusion Models for Reinforcement Learning: A Survey](https://mlsanity.com/paper/2311.01223/) (2023)
- [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)
- [Tutorial on Diffusion Models for Imaging and Vision](https://mlsanity.com/paper/2403.18103/) (2024)
- [Backprop KF: Learning Discriminative Deterministic State Estimators](https://mlsanity.com/paper/1605.07148/) (2016)
- [DiffuserLite: Towards Real-time Diffusion Planning](https://mlsanity.com/paper/2401.15443/) (2024)
- [AlignDiff: Aligning Diverse Human Preferences via Behavior-Customisable Diffusion Model](https://mlsanity.com/paper/2310.02054/) (2023)
- [Multimodal Sensor Fusion with Differentiable Filters](https://mlsanity.com/paper/2010.13021/) (2020)
- [How to Train Your Differentiable Filter](https://mlsanity.com/paper/2012.14313/) (2020)
- [DualSMC: Tunneling Differentiable Filtering and Planning under Continuous POMDPs](https://mlsanity.com/paper/1909.13003/) (2019)
- [Differentiable Factor Graph Optimization for Learning Smoothers](https://mlsanity.com/paper/2105.08257/) (2021)
- [Differentiable Particle Filters through Conditional Normalizing Flow](https://mlsanity.com/paper/2107.00488/) (2021)
- [Interpreting Contact Interactions to Overcome Failure in Robot Assembly Tasks](https://mlsanity.com/paper/2101.02725/) (2021)
- [DroneDiffusion: Robust Quadrotor Dynamics Learning with Diffusion Models](https://mlsanity.com/paper/2409.11292/) (2024)
- [Enhancing State Estimation in Robots: A Data-Driven Approach with Differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2308.09870/) (2023)
- [Differentiable Bootstrap Particle Filters for Regime-Switching Models](https://mlsanity.com/paper/2302.10319/) (2023)

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

- [DiffPF: Differentiable Particle Filtering with Generative Sampling via Conditional Diffusion Models](https://mlsanity.com/paper/2507.15716/) (2025)

## Abstract (arXiv)

This paper proposes the DnD Filter, a differentiable filter that utilizes diffusion models for state estimation of dynamic systems. Unlike conventional differentiable filters, which often impose restrictive assumptions on process noise (e.g., Gaussianity), DnD Filter enables a nonlinear state update without such constraints by conditioning a diffusion model on both the predicted state and observational data, capitalizing on its ability to approximate complex distributions. We validate its effectiveness on both a simulated task and a real-world visual odometry task, where DnD Filter consistently outperforms existing baselines. Specifically, it achieves a 25% improvement in estimation accuracy on the visual odometry task compared to state-of-the-art differentiable filters, and even surpasses differentiable smoothers that utilize future measurements. To the best of our knowledge, DnD Filter represents the first successful attempt to leverage diffusion models for state estimation, offering a flexible and powerful framework for nonlinear estimation under noisy measurements.