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

A new study by researchers Ali Siahkoohi and Davide Sabeddu tackles a critical, often overlooked problem in applying AI to geophysics. The paper, 'On the role of memorization in learned priors for geophysical inverse problems,' investigates how deep generative models—specifically diffusion models—used to regularize complex tasks like seismic inversion can fail. Because these models are trained via maximum likelihood on inherently scarce datasets of subsurface models, they risk simply memorizing the training examples. This memorization means the model converges to the empirical data distribution rather than learning the broader, underlying geological principles.

The authors demonstrate that when this memorization occurs, the model's posterior distribution—its refined guess after seeing new data—collapses into a reweighted version of the training set. For diffusion models, they derive a closed-form Gaussian mixture prior from memorization. More practically, when applied to a real-world technique like full waveform inversion (FWI), this flaw means the AI's output is essentially performing a 'likelihood-weighted lookup' among its memorized examples, governed by the local Jacobian of the forward operator. The team validated these theoretical predictions on a stylized inverse problem, showing the tangible consequences for the accuracy and generalizability of AI-powered subsurface imaging.