The paper introduces LUD-DIF, a diffusion-based method that solves inverse problems using unpaired data. By deriving the evidence lower bound of the joint distribution and decoupling it into two independent diffusion processes under a weak‑coupling assumption, the authors provide a variational inference framework, a loss function, and an error‑bound analysis. Experiments show that LUD‑DIF performs well across multiple image inverse problems, demonstrating its effectiveness and generalization in unpaired settings.
arXiv:2605.09477v2 Announce Type: replace-cross Abstract: Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based m...
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:2601. 22443v2 Announce Type: replace Abstract: Can a diffusion model trained on bedrooms recover human faces?
The paper introduces an active diffusion-based inverse problem solver that trains a diffusion model to map between parameter and observable spaces. By iteratively detecting and correcting model misspecification through posterior uncertainty, the method can discover and learn the correct parameter region even when initial training bounds exclude the true parameters. The authors demonstrate the solver on a toy inverse problem with infinite solutions and on parameterizing quantum correlation functions for a Quantum Chromodynamics analysis of nucleon structure.
arXiv:2607. 19333v1 Announce Type: cross Abstract: Diffusion-based methods have achieved remarkable empirical success in solving inverse problems.
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. 11711v2 Announce Type: replace-cross Abstract: This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems.
arXiv:2510. 02208v3 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative priors for solving inverse imaging 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:2507. 07008v2 Announce Type: replace Abstract: Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature.
arXiv:2606. 02331v1 Announce Type: cross Abstract: Diffusion-based inverse problem solvers can produce realistic reconstructions, but realism alone does not ensure that the recovered details are supported by the measurement.
arXiv:2410. 02628v5 Announce Type: replace Abstract: Learning conditional distributions $\pi^*(\cdot|x)$ is a central problem in machine learning, which is typically approached via supervised methods with paired data $(x,y) \sim \pi^*$.