arXiv:2606. 25169v2 Announce Type: replace-cross Abstract: Sampling from an unnormalized target by reversing an Ornstein-Uhlenbeck diffusion requires the score of each noise-perturbed marginal.
arXiv:2606. 25169v1 Announce Type: cross Abstract: Sampling from an unnormalized target by reversing an Ornstein--Uhlenbeck diffusion requires the score of each noise-perturbed marginal.
arXiv:2608. 01547v1 Announce Type: cross Abstract: Drifting objectives compare a target and model distribution through a vector field observed noisily at finitely many locations.
arXiv:2608. 15144v1 Announce Type: cross Abstract: Posterior sampling with a pretrained diffusion prior is governed by a conditional score whose intermediate likelihood component is generally intractable.
arXiv:2606. 17048v1 Announce Type: new Abstract: Diffusion and flow-based models learn powerful data priors by training a denoiser to reverse Gaussian corruption.
PosteriorBench is a new benchmark that evaluates how well generative inverse solvers recover full posterior distributions rather than just a single reconstruction. It tests four physics-based inverse problems—Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference—using high-fidelity reference posteriors generated by rejection sampling and MCMC. The benchmark employs five metrics (posterior-mean error, posterior-standard-deviation error, maximum mean discrepancy, sliced Wasserstein distance, and radially averaged power-spectrum error) to assess pointwise accuracy, uncertainty, distributional alignment, and global frequency fidelity, revealing significant distribution-matching gaps in current solvers and highlighting the importance of neural operators, guidance weights, and generation noise for posterior-variance calibration.
arXiv:2510. 12744v2 Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density.
The paper presents a method that combines flow‑matching models with energy‑based modeling to explicitly construct scalar energy functions for physical fields. These energies are derived from a matching regression objective on a linear Gaussian interpolation, avoiding variational approximations or extra MCMC steps, and can be used for energy‑corrected data generation, out‑of‑distribution detection, and posterior sampling in inverse problems. The approach enables general MCMC samplers that reduce PDE residuals and spectral distance, and it demonstrates that combining data‑driven and physics‑based energies improves OOD detection accuracy.
arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).
The paper introduces a two‑step debiased estimation method for PDE‑constrained inverse problems where the PDE solution is approximated by Physics‑Informed Neural Networks (PINNs). By combining neural‑network‑based nonparametric estimation with an influence‑function bias correction, the authors achieve a √{n}-consistent, asymptotically normal estimator without undersmoothing the neural network. The approach is extended to Bayesian inference, yielding a posterior that contracts at the √{n}-rate with asymptotic covariance matching the frequentist estimator, and the analysis also provides near‑minimax rates for estimating nonparametric regression functions and their derivatives in Sobolev spaces.
arXiv:2606. 30230v1 Announce Type: cross Abstract: Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training.
arXiv:2609.25145v1 Announce Type: cross Abstract: Variational autoencoders (VAEs) offer an efficient approach to amortized Bayesian inference for inverse problems, but posterior accuracy can depend s...
FB‑GDM is a fully‑Bayesian guided diffusion method that eliminates the need for task‑specific hyperparameter tuning in linear inverse problems. It derives a closed‑form conditional score from a Gaussian approximation of ΦGDM, treating two precision parameters as latent variables inferred via variational inference at each reverse step. Experiments on CelebA‑HQ show that FB‑GDM outperforms ΦGDM at its nominal setting, matches a ground‑truth‑calibrated oracle within 0.1 dB, and remains robust to changes in the forward operator, noise level, or image distribution without hallucinations.