Spatial prediction is a key task in analyses of spatially or spatio-temporally referenced data, typically handled with hierarchical models that combine a process model and a data model. The predictive distribution—conditional on observed data—is often intractable, but guided diffusion modeling from machine learning can sample from it when the likelihood is known and differentiable. The authors demonstrate this approach on Gaussian and non‑Gaussian processes, various data models (direct observations, aggregates, counts, censoring, area‑exceedance), validate against exact and MCMC results, and apply it to methane‑flux inversion over the UK and Ireland, showing accurate sampling, applicability to intractable MCMC cases, and good scalability with dimensionality.
arXiv:2609.00279v1 Announce Type: cross Abstract: This work shows that diffusion models learned with standard denoising loss can provide effective global MCMC proposals for complex high-dimensional t...
arXiv:2606. 14570v1 Announce Type: cross Abstract: Emulators provide a cost-effective alternative to regional climate models (RCMs) by capturing their dynamical downscaling function.
The paper introduces a transformer-based framework that learns an in‑context score operator for diffusion models, allowing the model to perform reverse‑diffusion sampling on unseen target distributions specified by a small empirical context set. By representing the task‑dependent score as a Gaussian‑kernel conditional mean and approximating it with a transformer‑based query‑dependent attention architecture, the method can adapt to new tasks without retraining or parameter updates. The authors provide theoretical generalization‑error bounds and evaluate the approach on scientific and visual datasets, noting strong performance on simple task families and limitations as task complexity grows.
arXiv:2606. 14313v1 Announce Type: cross Abstract: Real-world spatio-temporal forecasting must handle irregular time points, spatially sparse observations, and the need for uncertainty quantification.
arXiv:2512. 20685v3 Announce Type: replace-cross Abstract: Diffusion models have recently emerged as powerful learners for simulation-based inference (SBI), enabling fast and accurate estimation of latent parameters from simulated and real data.
arXiv:2610.19802v1 Announce Type: new Abstract: Negative guidance of diffusion models generates samples that avoid an undesired condition, specified either by reference samples or by a conditional sc...
arXiv:2606. 04324v1 Announce Type: new Abstract: One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the transition density function between consecutive observation times, which is needed to derive the likelihood function.
The paper introduces a new Markov chain Monte Carlo method that samples from multimodal distributions by interpolating along the diffusion path of a noising diffusion process, preserving mode weights and improving mixing. It proposes a Metropolis-adjusted diffusion path (MAD-Path) sampler that corrects for bias from approximate score estimates and discretization errors, ensuring the target distribution remains invariant. Experiments on Bayesian posteriors demonstrate that MAD-Path outperforms tempering-based MCMC and unadjusted diffusion samplers in global exploration and accurate mode-weight estimation.
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:2607. 08041v1 Announce Type: new Abstract: How diffusion models circumvent the curse of dimensionality to learn complex distributions over high dimensional spaces from a finite training set, instead of memorizing it, remains a fundamental mystery.
One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the transition density function between consecutive observation times, which is needed to derive the likelihood function. Extending previous studies that solve Fokker-Planck (FP) type partial differential equations with Normalizing Flows, we propose a new Normalizing Flow architecture to learn the transition density function of the diffusion process between two observation times.
arXiv:2601. 08379v2 Announce Type: replace-cross Abstract: Pre-trained diffusion models have emerged as powerful generative priors for both unconditional and conditional sample generation, yet their outputs often deviate from the characteristics of user-specific target data.