arXiv Machine Learning
Aug 3
Provable Diffusion Posterior Sampling for Bayesian Inversion
arXiv:2512. 08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework.
Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors
arXiv:2510. 10968v3 Announce Type: replace Abstract: Derivative-free Bayesian inversion arises in science and engineering applications, particularly when forward model is costly or infeasible to differentiate through.
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arXiv Machine Learning
Jun 26
Latent Diffusion Posterior Sampling with Surrogate Likelihood Guidance for PDE Inverse Problems
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).
arXiv Machine Learning
Sep 17
A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
arXiv:2509.19276v2 Announce Type: replace-cross Abstract: Solving ill-posed inverse problems requires powerful and flexible priors. We propose leveraging pretrained latent diffusion models for this t...
arXiv Machine Learning
Sep 18
PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers
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 AI
3d ago
Flow Annealing Posterior Sampling for Function-Space Regression and Inverse Problems
arXiv:2606.22346v2 Announce Type: replace-cross Abstract: Principled regression for stochastic processes is a long-standing challenge with deep connections to scientific inverse problems. We introduc...
arXiv Machine Learning
Sep 15
Backward SDEs-based Diffusion for Physics-Constrained Generation
arXiv:2609.15702v1 Announce Type: new Abstract: Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is of...
arXiv AI
Jun 30
DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing
arXiv:2511. 17038v4 Announce Type: replace Abstract: From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process.
arXiv Machine Learning
Aug 14
Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks
arXiv:2605. 07060v3 Announce Type: replace-cross Abstract: Physics-informed neural networks (PINNs) provide a mesh-free framework for solving PDE-constrained inverse problems, but their extension to Bayesian inversion still faces a fundamental difficulty: prior distributions are typically defined in the weight space of neural networks, whereas physically meaningful prior assumptions are more naturally expressed in function space.
arXiv Machine Learning
Jun 2
Preconditioned One-Step Generative Modeling for Bayesian Inverse Problems in Function Spaces
arXiv:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.
arXiv AI
Jul 22
Provable diffusion-based posterior sampling for linear inverse problems via DDIM
arXiv:2607. 19333v1 Announce Type: cross Abstract: Diffusion-based methods have achieved remarkable empirical success in solving inverse problems.
arXiv AI
Jul 20
Energy-based Transport for Amortized Bayesian Inference
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
arXiv Machine Learning
Jun 19
Neural network surrogates with uncertainty quantification for inverse problems in partial differential equations
arXiv:2606. 20417v1 Announce Type: new Abstract: Inverse problems for differential equations arise throughout science and engineering, where one seeks to infer unknown model parameters from noisy or incomplete observations.