We propose an approach to build and sample surrogate stochastic models leveraging state-of-the-art score-based diffusion approaches, either abstracting a known stochastic process or learning directly the model from data. In particular, we propose a method for efficient conditional sampling from such surrogate models, enforcing logical and consistency constraints on generated samples in a soft fashion. As a preliminary case study, we consider a surrogate SIR model, in both its ergodic and non-ergodic formulations. Using the aforementioned method, we are able to sample trajectories from such models that exhibit desirable features having low probability in the unconstrained models, allowing us to explore epidemiologically relevant scenarios. Although the proposed approach is still a work-in-progress, it has significant potential for applications in epidemiology and other fields. The method is also efficient in the sense that retraining is not needed to generate samples satisfying different constraints.
