Stochastic reconstruction of gappy Lagrangian turbulent signals by conditional diffusion models

Understanding and predicting the motion of small objects in turbulent flows is essential for applications in atmospheric science and oceanography. However, missing velocity data along their trajectories remains a major challenge. Here, we present a stochastic method that uses generative diffusion models to reconstruct missing velocity data for objects passively advected by turbulent flows, such as balloons in the atmosphere or oceanic drifters. We show that this method successfully reconstructs both three-dimensional trajectories in homogeneous isotropic turbulence and two-dimensional trajectories from real-world ocean data. The reconstructed signals retain complex scale-by-scale features that are highly non-Gaussian and intermittent. Our approach outperforms Gaussian process regression in both pointwise accuracy and statistical fidelity. We also analyze its generalization to different datasets, robustness to noise, and computational efficiency. This method opens new possibilities for improving data quality in environmental monitoring and advancing our understanding of turbulent transport.