On the role of memorization in learned priors for geophysical inverse problems
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915876559650816 |
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| author | Siahkoohi, Ali Sabeddu, Davide |
| author_facet | Siahkoohi, Ali Sabeddu, Davide |
| contents | 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 sampling for full waveform inversion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19629 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the role of memorization in learned priors for geophysical inverse problems Siahkoohi, Ali Sabeddu, Davide Machine Learning Geophysics 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 sampling for full waveform inversion. |
| title | On the role of memorization in learned priors for geophysical inverse problems |
| topic | Machine Learning Geophysics |
| url | https://arxiv.org/abs/2603.19629 |