Teaching Gaussian processes to handle any constraint you can imagine

Gaussian processes are mathematically elegant for probabilistic modeling but break down when you try to condition on anything messier than linear relationships. Researchers connected GPs to diffusion models and showed the conditioning problem becomes an ODE with closed-form solutions, enabling a single Monte Carlo algorithm that handles nonlinear physics constraints, LLM-based constraints, and traditional data simultaneously. No more deriving custom inference for each problem type.