Noise-Informed Conformal Prediction for Trajectory World Models

Trajectory world models are predictive models that learn complex dynamics of diverse robotic systems from low-level states. Quantifying the uncertainty of trajectory world models is critical to ensuring the safety and reliability of downstream control and planning tasks. Conformal prediction (CP) is a model-agnostic uncertainty quantification framework with formal calibration guarantees, making it widely applicable to various learning-based dynamics models. However, trajectory data collected from robotic systems are inevitably affected by unbounded and temporally correlated observation noise, leading to an underestimation of the model’s true prediction error. In such scenarios, existing methods cannot provide calibrated prediction sets for the system’s true future states. To address this challenge, we propose Noise-Informed Conformal Prediction (NICP), which constructs an auxiliary covariance matrix by applying a covariance mapping to the noise information provided by the state estimator and then draws samples according to it to augment the observed prediction errors, thereby mitigating the underestimation of the model's true prediction error. Moreover, under certain conditions, we prove that the proposed method provides prediction sets with finite-sample marginal coverage guarantees. Experiments across different trajectory world models and both simulated and real-world robotic tasks show that our method can provide calibrated uncertainty estimates under noisy observations, while existing CP methods suffer from significant underestimation or overestimation in this setting.