New GP Inference Method Conditions on Language and Physics

Gaussian processes (GPs) have long been a cornerstone of probabilistic modeling, but their power was limited to linear-Gaussian conditioning. A new paper by Moss et al. shatters that constraint by showing an explicit equivalence between GPs and a class of linear diffusion models. This recasts predictive sampling as an ODE with closed-form Gaussian dynamics plus a likelihood-dependent guidance term approximated via Monte Carlo. In the linear-Gaussian case, standard GP conditioning is recovered exactly. Beyond conjugacy, the same machinery handles any conditioning statement that admits pointwise likelihood evaluation—covering nonlinear physics and, for the first time, natural language via large language models. Whitening isolates irreducible non-Gaussian dynamics, minimizing Wasserstein-2 transport cost and eliminating numerical stiffness. The result is a general-purpose GP inference scheme requiring no bespoke derivations.

This breakthrough means practitioners can now incorporate the full richness of real-world knowledge—text, constraints, physics simulations—into GP models without custom math. For example, an engineer could condition a GP on a partial differential equation and text descriptions simultaneously. The approach also promises seamless integration with LLMs, enabling probabilistic models that reason about language as naturally as about numerical data. While the paper is theoretical, the method’s simplicity hints at rapid adoption in fields like Bayesian optimization, robotics, and scientific computing. The authors have made the code available, and the community is already buzzing about applications from drug discovery to climate modeling.