arXiv:2509. 03910v2 Announce Type: replace-cross Abstract: We formulate inverse problems in a Bayesian framework and aim to train an invertible generative model that is capable of simulation (i.
arXiv:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.
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.
The paper introduces a continuous normalizing flow model for infinite-dimensional Bayesian inference in inverse problems governed by partial differential equations. By defining a neural ordinary differential equation in an infinite-dimensional Hilbert space, a simple reference measure is transformed into a complex prior that captures prior information. The authors establish a theoretical framework for well-posedness, present training methods for two data settings, and provide sampling algorithms, applying the approach to smooth, scattering, and heat conduction inverse problems with supporting numerical experiments.
arXiv:2609.37529v1 Announce Type: cross Abstract: Pretrained denoisers provide a powerful way to incorporate image priors into restoration algorithms. Plug-and-Play and RED approaches exploit fixed-n...
FlowSGS introduces a flow-based posterior sampling method that combines Split Gibbs Sampling (SGS) with Langevin dynamics for the likelihood step and Stochastic Interpolants (SI) for the prior step. By integrating a pretrained flow model into the prior step via SI's reverse-time SDE and a novel timestep correction, FlowSGS reduces the number of network evaluations compared to plug‑and‑play diffusion samplers. Experiments demonstrate state‑of‑the‑art performance on various inverse problems, including the first flow‑based solution to a nonlinear inverse problem (Fourier phase retrieval).
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.
The paper introduces the Ensemble-conditioned Inverse Problem (EIP), a multivariate statistical framework for inferring an ensemble that follows the pushforward of a prior through a forward process. It applies to fields such as high‑energy physics, full waveform inversion, and inverse imaging, and proposes non‑iterative inference‑time methods using ensemble inverse generative models that avoid explicit forward model use during inference. The authors demonstrate the approach on synthetic and real datasets and provide code for replication.
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: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: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.
arXiv:2602. 11711v2 Announce Type: replace-cross Abstract: This article addresses the issue of estimating observation parameters (response and error parameters) in 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.