An invertible generative model for forward and inverse problems

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.

A Gibbs posterior sampler for inverse problem based on prior diffusion model

arXiv:2602. 11059v2 Announce Type: replace-cross Abstract: This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive error, (2) the problem is ill-posed and regularization relies on a Bayesian strategy, (3)~the prior is modeled by a diffusion process adjusted on an available large set of examples.

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.

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).

P-Flow: Proxy-gradient Flows for Linear Inverse Problems

arXiv:2605. 08328v3 Announce Type: replace Abstract: Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models.

Estimation of instrument and noise parameters for inverse problem based on prior diffusion model

arXiv:2602. 11711v2 Announce Type: replace-cross Abstract: This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems.

A Convex Approximation Framework for Neural Likelihood-Based Bayesian Inverse Problems

arXiv:2607. 06252v1 Announce Type: cross Abstract: Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations.

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.

Dual-space posterior sampling for Bayesian inference in constrained inverse problems

arXiv:2603. 00393v2 Announce Type: replace-cross Abstract: Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy, incomplete data or inherent non-uniqueness.

FFJORD: Free-form continuous dynamics for scalable reversible generative models

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.

Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems

arXiv:2508. 09156v3 Announce Type: replace-cross Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.