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

Abstract: 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.