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: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:2609.14596v1 Announce Type: new Abstract: Training-free diffusion inverse solvers typically choose between local measurement guidance and costly clean-space posterior updates. Independent poste...
The paper introduces MS-Flow, a method that represents a flow-based generative model’s trajectory as a sequence of intermediate latent states instead of a single initial code. By enforcing local flow dynamics and coupling trajectory segments with matching penalties, the approach alternates between updating latent states and ensuring consistency with observed data. This strategy reduces memory usage and improves reconstruction quality on tasks such as image inpainting, super‑resolution, and computed tomography.
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:2607. 19333v1 Announce Type: cross Abstract: Diffusion-based methods have achieved remarkable empirical success in solving inverse problems.
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.
EquiReg introduces an equivariance‑regularized diffusion framework that penalises sampling trajectories deviating from the data manifold, thereby improving posterior sampling for inverse problems. By formalising manifold‑preferential equivariant functions—naturally arising from data augmentation or inherent symmetries—EquiReg guides diffusion steps toward symmetry‑preserving regions of the solution space. The method shows consistent gains in both linear and nonlinear image restoration tasks and partial differential equation solving, especially under reduced sampling and measurement consistency steps, and is available as open‑source code.
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:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.
arXiv:2606. 17048v1 Announce Type: new Abstract: Diffusion and flow-based models learn powerful data priors by training a denoiser to reverse Gaussian corruption.
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.