Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse Problem

arXiv:2609.03343 · math.NA, cs.LG, cs.NA · Submitted 2026-09-03 · Read on arXiv

math.NA, cs.LG, cs.NA

Submitted: 2026-09-03

Updated: 2026-09-23

Terminology

• Inverse Problem — 74× in this paper · explained in 2 episodes
• Normalizing Flow — 47× in this paper · explained in 3 episodes
• Normalizing Flows — 17× in this paper · explained in 4 episodes
• Diffusion Model — 11× in this paper · explained in 8 episodes
• Diffusion Models — 10× in this paper · explained in 6 episodes
• Hilbert Space — 10× in this paper · explained in 2 episodes
• Loss Function — 7× in this paper · explained in 2 episodes
• Bayesian Framework — 6× in this paper · explained in 3 episodes
• Bayesian Inference — 6× in this paper · explained in 5 episodes
• Generative Model — 6× in this paper · explained in 2 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Generalization — 4× in this paper · explained in 13 episodes
• Uncertainty Quantification — 4× in this paper · explained in 8 episodes
• Generative Models — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Computational overhead — 2× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Meta-learning — 2× in this paper · explained in 2 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Variational Bayes — 2× in this paper · explained in 2 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Calibration — 1× in this paper · explained in 7 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generalization Bounds — 1× in this paper · explained in 2 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Score Function — 1× in this paper · explained in 4 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes
• Verification — 1× in this paper · explained in 2 episodes
• Wasserstein Distance — 1× in this paper · explained in 4 episodes

Sources

• Sequential Monte Carlo with Gaussian Mixture Approximation for Infinite-Dimensional Statistical Inverse Problems
• Functional normalizing flow for statistical inverse problems of partial differential equations

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