The paper introduces improvements to FlowGP, a method for conditional sampling from Gaussian processes outside the linear-Gaussian regime. It adds kernel approximations to scale to high-resolution domains and a new technique for computing marginal likelihood by measuring the work required to steer diffusion toward conditioning statements. These advances enable hyperparameter optimisation within FlowGP and are demonstrated on tasks such as probabilistic downscaling, PDE solution inference on irregular domains, and sea level anomaly field recovery from non-Gaussian satellite data.
arXiv:2607. 19498v1 Announce Type: cross Abstract: Gaussian process (GP) modeling is widely used in computational science and engineering.
arXiv:2610.03201v1 Announce Type: cross Abstract: Gaussian Processes (GPs) are a powerful tool for modelling and quantifying uncertainty in functional relationships. However, they require practitione...
The paper introduces a structured posterior‑correction framework that blends a tractable Gaussian reference with data‑driven corrections learned via diffusion models. After applying mean correction and covariance calibration, the diffusion model focuses on a low‑dimensional subspace that captures discrepancies from the Gaussian reference, while the remaining space stays Gaussian. Experiments on three scientific inference tasks show that these corrections recover hidden modes, improve sample structure, and reduce prediction error compared to the Gaussian reference, with trade‑offs between accuracy and computational cost relative to full‑field generative models.
arXiv:2511. 16340v2 Announce Type: replace Abstract: Efficient Gaussian process (GP) inference is critical for sequential decision-making tasks such as active learning, online prediction, and Bayesian optimization.
arXiv:2605. 10285v2 Announce Type: replace-cross Abstract: We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels.
The paper introduces a scalable Bayesian method for conditional density estimation using a logistic Gaussian process. It models the log conditional density with a separable covariance— a Matérn kernel on the response dimension and a Nyström-feature kernel on covariates— and samples the latent field via kinetic Langevin dynamics instead of traditional approximations. Experiments on photometric‑redshift data with up to 3.9 million observations show the approach matches state‑of‑the‑art tabular foundation models on density and calibration metrics.
The paper introduces a scalable variational inference framework for latent field models with non‑Gaussian likelihoods. It mirrors the sparse nearest‑neighbor autoregressive structure of the Gaussian process prior in the variational family, employs normalizing‑flow conditionals for expressiveness, and amortizes all variational parameters through a single shared neural conditioner. The method achieves polylogarithmic per‑iteration complexity via doubly stochastic optimization with reduced ancestor sets.
arXiv:2602.19600v2 Announce Type: replace Abstract: Many high-dimensional datasets concentrate near a low-dimensional structure embedded in the ambient space. Generative models for such data must con...
arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.
The paper introduces Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models, enabling the variational posterior over latent variables to depend on GP inducing points. This approach addresses limitations of mean‑field approximations and yields improved reconstruction metrics for data manifold points.
arXiv:2512. 06143v2 Announce Type: replace Abstract: Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists.
arXiv:2608. 01793v1 Announce Type: new Abstract: Unified anomaly detection requires modeling highly heterogeneous normal data without access to anomalous samples.