Inverse Problems
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Related Articles from SNS
Constraint residuals, graph posteriors, and determinant-corrected full-space targets in Bayesian inverse problems
Announce Type: cross Abstract: Bayesian inverse problems constrained by state equations are often sampled in a full parameter-state space by penalising the residual, rather than in a reduced space where the state is eliminated. We show that these formulations are not automatically equivalent as posterior measures. For finite-dimensional discretisations of equality-constrained inverse problems, assume the state equation \(c(\theta,u)=0\) has a unique solution \(u=G(\theta)\) and nonsingular...
A Unified DeepONet Framework for Logarithmically Stable Infinite-Dimensional Inverse Problems
arXiv:2606.07122v1 Announce Type: new Abstract: We develop a unified DeepONet framework for logarithmically stable infinite-dimensional inverse problems, with inverse acoustic scattering as a model application. The framework is formulated at the operator level by separating the learned inverse map into measurement encoding, finite-dimensional neural approximation, and functional reconstruction components. For inverse maps satisfying a logarithmic stability estimate, we establish quantitative...
Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems
arXiv:2605.29373v2 Announce Type: replace Abstract: Solving high-dimensional PDE-governed inverse problems is often challenging due to complex non-Gaussian posterior distributions, expensive forward model evaluations, and misspecified prior information. To address these issues, we propose a deep adaptive dimension-reduction Bayesian inference framework based on the Variational Flow (VF) model. Since standard normalizing flows are restricted by bijective mappings and cannot directly reduce...
Measurement Geometry and Design for Trustworthy Generative Inverse Problems
arXiv:2606.02309v1 Announce Type: new Abstract: Generative models are increasingly used as priors for inverse problems, but their ability to produce realistic images creates a basic trust problem: a plausible reconstruction may be supported by the measurements, or it may be filled in by the prior along unobserved directions. This distinction is especially important in medical imaging, where acquisition operators are designed under scan-time, dose, and calibration constraints. We study...
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. Based on one-step generative transport, the method learns an amortized neural operator whose pushforward of a Gaussian source approximates the posterior distribution conditioned on each new observation. We show that white-noise sources are incompatible with the function-space limit, and therefore adopt a prior-aligned GRF as the source.
Hallucination-Aware Diffusion Sampling for Inverse Problems via Robust Prior Updates
arXiv:2606.02331v1 Announce Type: new 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. We study this failure as measurement-conditioned hallucination: visually meaningful content that is either implausible or inconsistent with the measured instance. Our analysis separates Bayes-rule-based diffusion inverse solvers into a prior update and a...
Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solvers
arXiv:2601.04791v4 Announce Type: replace Abstract: While latent diffusion models (LDMs) have emerged as powerful priors for inverse problems, existing LDM-based solvers frequently suffer from instability. In this work, we first identify the instability as a discrepancy between the solver dynamics and stable reverse diffusion dynamics learned by the diffusion model, and show that reducing this gap stabilizes the solver. Building on this, we introduce \textit{Measurement-Consistent Langevin...
Solving Inverse Problems with Flow-based Models via Model Predictive Control
arXiv:2601.23231v2 Announce Type: replace-cross Abstract: Flow-based generative models provide strong unconditional priors for inverse problems, but guiding their dynamics for conditional generation remains challenging. Recent work casts training-free conditional generation in flow models as an optimal control problem; however, solving the resulting trajectory optimisation is computationally and memory intensive, requiring differentiation through the flow dynamics or adjoint solves. We...
KLIP: localized distribution shift detection via KL-divergence with diffusion priors in Inverse Problems
arXiv:2605.31596v1 Announce Type: new Abstract: Diffusion models have shown promising performance as data-driven priors for computational imaging, as well as some capacity to detect out-of-distribution (OOD) images. However, existing approaches to OOD detection often require some knowledge of the shifted distribution, fail to detect subtle or localized distribution shifts, and operate on full images, rather than the indirect measurements available in inverse problems. We propose an OOD...
From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models
arXiv:2606.08956v1 Announce Type: new Abstract: Scientists have historically relied on mathematical models based on differential equations to relate system inputs -- forces, fluxes, or heat sources -- to outputs, such as displacement, velocity, concentration, and temperature. These models rely on deep domain knowledge to determine the form of the governing differential equation, which is then calibrated with data by solving an inverse problem. In recent years, the field of Scientific Machine...