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: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...
arXiv:2601. 21284v2 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in engineering and scientific problems where physical laws must be respected.
arXiv:2610.01759v1 Announce Type: new Abstract: Generating and predicting spatiotemporal physical fields from scarce measurements is challenging, as observations are insufficient to characterize a di...
arXiv:2606. 10023v1 Announce Type: cross Abstract: Accurate posterior estimation is central to scientific inference, as uncertainties determine what can be reliably learned from observational data.
arXiv:2607. 19498v1 Announce Type: cross Abstract: Gaussian process (GP) modeling is widely used in computational science and engineering.
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.
The paper introduces Latent Annealed Posterior Sampling (LAPS), a method that maps sparsely observed random fields into a lower‑dimensional latent space and performs posterior sampling there. A variance‑preserving bridge controls local covariance inflation, while flow matching learns the latent prior. Experiments on Gaussian benchmarks, a bimodal posterior, and a Navier‑Stokes field show that LAPS accurately approximates posterior distributions, preserves multiple modes, and keeps conditional sampling costs nearly constant as spatial resolution increases.
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:2608.21729v1 Announce Type: new Abstract: Simulation-Based Inference (SBI) serves as a vital framework for parameter inference in scientific fields where simulators involve intractable likeliho...
arXiv:2608. 07648v1 Announce Type: cross Abstract: Sampling high-dimensional probability distributions is a central task in scientific computing, with applications ranging from Bayesian inference to statistical physics and molecular simulation.
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.
arXiv:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.