State estimation remains a fundamental challenge across numerous domains, from autonomous driving, aircraft tracking to quantum system control. Although Bayesian filtering has been the cornerstone solution, its classical model-based paradigm faces two major limitations: it struggles with inaccurate state space model (SSM) and requires extensive prior knowledge of noise characteristics. We present TrackDiffuser, a generative framework addressing both challenges by reformulating Bayesian filtering as a conditional diffusion model. Our approach implicitly learns system dynamics from data to mitigate the effects of inaccurate SSM, while simultaneously circumventing the need for explicit measurement models and noise priors by establishing a direct relationship between measurements and states. Through an implicit predict-and-update mechanism, TrackDiffuser preserves the interpretability advantage of traditional model-based filtering methods. Extensive experiments demonstrate that our framework substantially outperforms both classical and contemporary hybrid methods, especially in challenging non-linear scenarios involving non-Gaussian noises. Notably, TrackDiffuser exhibits remarkable robustness to SSM inaccuracies, offering a practical solution for real-world state estimation problems where perfect models and prior knowledge are unavailable.

To explore safely in such environments, it is critical for robots to generate quick, yet smooth responses to any changes in the obstacles, map, and environment. In this paper, we propose a means to design and compose control barrier functions (CBFs) for multiple non-overlapping obstacles and evaluate the system on a 20-degree-of-freedom (DoF) bipedal robot. In an autonomous system, the task of avoiding obstacles is usually handled by a planning algorithm because it has access to the map of an entire environment. Given the map, the planning algorithm is then able to design a collision-free path from the robot's current position to a goal. If the map is updated due to a change in the environment, the planner then needs to update the planned path, so-called replanning, to accommodate the new environment. Such maps are typically large and contain rich information such as semantics, terrain characteristics, and uncertainty, and thus are slow to update. This raises a concern when obstacles either move into the planned path but the map has not been updated or a robot's new pose allows the detection of previously unseen obstacles. The slow update rate of the map leads to either collision or abrupt maneuvers to avoid collisions. The non-smooth aspects arising from the map updates or changes in the perceived environment can be detrimental to the stability of the overall system.