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.
arXiv:2605. 00941v4 Announce Type: replace Abstract: Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem.
The paper introduces β‑Flow, a versatile plug‑and‑play posterior sampling framework that unifies flow‑matching, diffusion, and decorrelated priors through a correlation parameter β and a confidence parameter κ. Each iteration requires only a single denoising network forward pass followed by an exact Gaussian conditioning step, implemented as a Kalman update independent of network gradients. The authors demonstrate that many existing guided samplers are special cases of β‑Flow, and show state‑of‑the‑art performance on seven inverse problems across four datasets, with the ability to tune prior strength based on data informativeness.
arXiv:2610.01034v1 Announce Type: cross Abstract: Bayesian inference increasingly uses informative but implicit priors represented only by samples, such as historical ensembles, simulator outputs, an...
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.
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:2609.37381v1 Announce Type: new Abstract: Neural simulation-based inference (SBI) has been widely successful in inferring a relatively small number of interpretable parameters from potentially...
arXiv:2606. 11140v1 Announce Type: cross Abstract: Data assimilation (DA) in subsurface flow entails calibrating model parameters to match observed data, typically at wells, while preserving geological realism.
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.
The paper tackles two shortcomings of Gaussian‑process based active learning: (1) the posterior variance is independent of observed values, reducing sensitivity to data structure, and (2) it over‑inflates variance near domain boundaries, causing excessive edge sampling. The authors propose a reconstruction‑driven design density that warps sampling toward regions where the posterior mean changes rapidly, and a geometric equalizer that corrects boundary bias. Experiments on sixteen synthetic and two real‑data benchmarks show that the equalizer consistently improves function reconstruction, while the warp further enhances performance by concentrating measurements where the target function varies most.
arXiv:2509. 23385v5 Announce Type: replace-cross Abstract: Simulation-based inference (SBI) is transforming experimental sciences by enabling parameter estimation in complex non-linear models from simulated data.
Hierarchical data is ubiquitous in the empirical sciences and is most commonly analyzed with generalized linear mixed-effects models (GLMMs). Bayesian inference for GLMMs yields calibrated uncertainty...
The paper introduces FREESIA, a training‑free, covariance‑aware posterior transport method for data assimilation that embeds forecast cross‑covariance into a flow‑based transport to recover unobserved states while preserving non‑Gaussian posterior structure. It combines an observation‑adaptive proposal with posterior correction, providing an asymptotically exact approximation of nonlinear posteriors and a Wasserstein error bound. Experiments on Double‑Well, Lorenz‑96, and Kolmogorov flow demonstrate that FREESIA captures complex posterior structures and achieves up to a 56% reduction in RMSE compared to the best baseline in sparse, nonlinear, non‑injective observation scenarios.