Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models, recasting predictive sampling as an ODE with closed-form Gaussian dynamics and a likelihood-dependent guidance term that admits a simple Monte Carlo approximation. In the linear-Gaussian setting, we recover standard GP conditioning exactly; beyond conjugacy, the same machinery handles any conditioning statement admitting point-wise likelihood evaluation — including non-linear physics, and, for the first time, natural language via large language models. Whitening isolates the irreducible non-Gaussian dynamics, minimising Wasserstein-2 transport cost and eliminating numerical stiffness. The result is a general-purpose GP inference scheme requiring no bespoke derivations. Together, these results provide a general mechanism for incorporating the full richness of real-world knowledge as conditioning information, opening a new frontier for the probabilistic modelling of real-world problems.

To date, Bayesian experimental design (BED) has largely studied how a single adaptive policy should choose experiments. Yet many real-world settings involve multiple designers making experimental decisions independently, including laboratories, field teams, and decentralised robots. Even when individual designers choose informative experiments, they may collectively acquire redundant information. In this talk, we introduce multi-designer Bayesian experimental design (MD-BED) and explore the coordination problem that arises when designers share an inferential objective but act using only their local histories. We show how this problem can be characterised information-theoretically, and how centralised training with decentralised execution (CTDE) can improve information acquisition and encourage designer specialisation under heterogeneous experimental costs, without requiring communication during execution.

This is where the abstract for the seminar goes.

This is where the abstract for the seminar goes.

This is where the abstract for the seminar goes.

This is where the abstract for the seminar goes.

This is where the abstract for the seminar goes.

This is where the abstract for the seminar goes.

This is where the abstract for the seminar goes.

This is where the abstract for the seminar goes.