arXiv Machine Learning
A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
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Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions
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 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 Computer Vision
Sep 18
FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolants
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 Machine Learning
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Weak Diffusion Priors Can Still Achieve Strong Inverse-Problem Performance
arXiv:2601. 22443v2 Announce Type: replace Abstract: Can a diffusion model trained on bedrooms recover human faces?
arXiv Machine Learning
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Provable Diffusion Posterior Sampling for Bayesian Inversion
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arXiv Computer Vision
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Diffusion Based Unpaired Data Learning for Inverse Problems
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.