With the rapid development of autonomous driving systems (ADSes), real-world roads are evolving into mixed-traffic environments where autonomous vehicles (AVs) and other traffic participants (e.g., human-driven vehicles (HDVs), cyclists, and pedestrians) coexist and interact with each other. However, current ADSes still incur various safety violations in mixed traffic scenarios, raising a strong demand for runtime safety assurance frameworks that can continuously monitor hazards and prevent potential violations. Existing ego-centric assurance approaches are insufficient for mixed traffic, where violations often arise from locally reasonable yet jointly incompatible decisions among multiple vehicles and cannot be reliably resolved through independent takeover. To bridge this gap, we propose CoSafe, a modular and ADS-agnostic cooperative runtime safety assurance framework for mixed-traffic autonomous driving to extend runtime safety assurance from ego-centric takeover to scene-level cooperative intervention. CoSafe leverages vehicle-to-everything (V2X) communication to enable roadside units (RSUs) to monitor scene-level hazards and jointly mitigate hazards involving multiple vehicles. We integrate CoSafe with seven state-of-the-art ADSes, and our evaluation on the InterDrive benchmark demonstrates that CoSafe improves the driving score of AVs by 70.03% on average, reduces safety violations by 87.80%, and accurately identifies unsafe AVs with an F3 score of 0.930, while satisfying real-time constraints.
Full waveform inversion (FWI) reconstructs subsurface velocity models from seismic mea surements but faces the challenges of ill-posedness and nonlinearity, making accurate inversion dependent on suitable initialization and effective prior constraints. Classical methods stabi lize the inversion and improve convergence by designing hand-crafted regularization terms, yet these terms provide limited descriptions of complex geological structures. Recent diffusion based methods learn more detailed structural priors from data and integrate them into inverse problem solvers. We propose Physical-State-Guided Diffusion Sampling (PSG), which decouples diffusion posterior sampling into two mutually interacting processes: regularized FWI optimiza tion and conditional diffusion sampling with linear guidance. PSG shows overall improvements in reconstruction accuracy, preservation of prior structure, and robustness over classical and diffusion-based baselines across diverse OpenFWI inversion scenarios. Through domain decom position, PSG can generalize without retraining to more complex, realistic velocity fields with structural patterns distinct from those represented by the prior learned from training datasets and larger spatial domains than the training models. Overall, PSG offers a flexible framework for integrating learned priors with physical constraints, with potential for extension to other nonlinear inverse problems.