Conditioning Gaussian Processes on Almost Anything
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. White...
| Authors | Henry Moss, Lachlan Astfalck, Thomas Cowperthwaite et al. |
|---|---|
| Primary category | stat.ML |
| Published | 20 May 2026 |
| Last updated at source | 20 May 2026 |
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