Geometry-conditioned diffusion generation of Lagrangian particle trajectories in human airways

Fast and subject-specific prediction of particle transport in the human airways is central to quantifying aerosol deposition, optimizing inhaled drug delivery, and supporting dose assessment in radiation research. While computational fluid and particle dynamics simulations provide high-fidelity trajectory data, their use in clinical or large-cohort settings remains limited by stringent geometric preprocessing (segmentation quality control, topology repair, surface smoothing, and meshing) and by the high computational cost of coupled airflow-particle tracking. Recent data-driven surrogates have accelerated aspects of airway flow prediction, but most approaches focus on Eulerian flow fields, operate in simplified or two-dimensional settings, and often struggle to generalize across complex three-dimensional anatomies. Especially for particle trajectories in a Lagrangian frame of reference, which are intrinsically multimodal and sensitive to local geometry. In this work we propose a geometry-conditioned guided denoising diffusion probabilistic model that generates physically plausible particle trajectories directly in a Lagrangian representation. Airway anatomy is encoded by a variational autoencoder to provide a compact conditioning latent, and geometric feasibility during sampling is reinforced through signed distance function guidance that discourages samples leaving the airway lumen. Despite training on particle-track data from only nine simulated airway geometries, the proposed method produces trajectory ensembles that qualitatively match ground-truth branching patterns and recover the underlying velocity magnitude statistics with good agreement, while guidance reduces non-physical wall-penetrating outliers. Remaining limitations include occasional boundary violations in challenging cases, and degraded behavior for out-of-distribution geometries not represented by the limited training set.