mlsanityData to 7 Oct 2026

Conditioning Gaussian Processes on Almost Anything

arXiv 2605.21041 ↗First posted 20 May 2026stat.ML cs.LG stat.MEcited by 3

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 36 of its 60 references that are in the map. First posted on arXiv 20 May 2026.

Builds on

36 of 60 references.

References · 36

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
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24 more
  1. 2023Manifold Preserving Guided Diffusioncited by 153
  2. 2026Qwen3.5-Omni Technical Reportcited by 146
  3. 2017Machine Learning of Linear Differential Equations using Gaussian Processescited by 139
  4. 2021Solving and Learning Nonlinear PDEs with Gaussian Processescited by 128
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  17. 2022Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equationscited by 14
  18. 2024Free Hunch: Denoiser Covariance Estimation for Diffusion Models Without Extra Costscited by 14
  19. 2024Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inferencecited by 8
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 1
  2. 2026Feature Space Adaptation for Effortless Gaussian Process Flowscited by 0
  3. 2026Ghost tasking for parametrized Gaussian Processes solving linear differential equationscited by 0

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