[2603.19629] On the role of memorization in learned priors for geophysical inverse problems

Statistics > Machine Learning arXiv:2603.19629 (stat) [Submitted on 20 Mar 2026] Title:On the role of memorization in learned priors for geophysical inverse problems Authors:Ali Siahkoohi, Davide Sabeddu View a PDF of the paper titled On the role of memorization in learned priors for geophysical inverse problems, by Ali Siahkoohi and Davide Sabeddu View PDF HTML (experimental) Abstract:Learned priors based on deep generative models offer data-driven regularization for seismic inversion, but training them requires a dataset of representative subsurface models -- a resource that is inherently scarce in geoscience applications. Since the training objective of most generative models can be cast as maximum likelihood on a finite dataset, any such model risks converging to the empirical distribution -- effectively memorizing the training examples rather than learning the underlying geological distribution. We show that the posterior under such a memorized prior reduces to a reweighted empirical distribution -- i.e., a likelihood-weighted lookup among the stored training examples. For diffusion models specifically, memorization yields a Gaussian mixture prior in closed form, and linearizing the forward operator around each training example gives a Gaussian mixture posterior whose components have widths and shifts governed by the local Jacobian. We validate these predictions on a stylized inverse problem and demonstrate the consequences of memorization through diffusion posterior ...