The field of inverse problems and generative modeling is witnessing significant advancements, driven by the development of novel methodologies and techniques. A key direction is the integration of diffusion models with other methods, such as Monte Carlo and Bayesian optimization, to improve the accuracy and efficiency of inverse problem solving. Another area of focus is the development of multi-fidelity and multi-physics approaches, which enable the incorporation of diverse data types and physical fields to enhance the robustness and reliability of predictions. Noteworthy papers in this area include: Blade, which introduces a derivative-free Bayesian inversion method using diffusion priors, achieving superior performance on various inverse problems. Y-shaped Generative Flows, which proposes a novel generative model that induces Y-shaped transport, recovering hierarchy-aware structure and improving distributional metrics over strong flow-based baselines.
Advancements in Inverse Problems and Generative Modeling
Sources
Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Sampling
Parameterized crack modelling based on a localized non-intrusive reduced basis method
Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors
A Constrained Multi-Fidelity Bayesian Optimization Method
Multi-Physics-Enhanced Bayesian Inverse Analysis: Information Gain from Additional Fields
An Eulerian Perspective on Straight-Line Sampling
Multi-objective Bayesian Optimization with Human-in-the-Loop for Flexible Neuromorphic Electronics Fabrication
Y-shaped Generative Flows
DiffEM: Learning from Corrupted Data with Diffusion Models via Expectation Maximization
On the prospects of interpolatory spline bases for accurate mass lumping strategies in isogeometric analysis
Unsupervised Constitutive Model Discovery from Sparse and Noisy Data
Progressive multi-fidelity learning for physical system predictions
Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey
On the convergence of stochastic variance reduced gradient for linear inverse problems
Augmented Lagrangian Method based adjoint space framework for sparse reconstruction of acoustic source with boundary measurements