Preconditioned One-Step Generative Modeling for Bayesian Inverse Problems
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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.