Score-based diffusion models are currently the most successful generative models for images and videos. They are also rapidly being adopted in scientific modelling of dynamic systems, such as climate & weather, earth system dynamics, and biomedical imaging. Of particular interest in such scientific applications is the ability to condition simulations on various forms of external information, such as censored observations of the trajectory, forcings, boundary conditions, etc. Methods for this purpose are being developed and employed across the community. We are planning to investigate this model class and application setting from theoretical, algorithmic, and practical perspectives. We will investigate methodological improvements to reduce the sampling and simulation cost of diffusion models; and test them on multiple different application domains. During the visit(s) to Amsterdam, Carla will work with Max on new ideas to produce commercial value from the new functionality and results developed during her time in Tübingen.