Yuke Xie

Nonlinear inverse problems in seismic imaging, particularly Full Waveform Inversion (FWI), are ill-posed and face challenges such as non-uniqueness, slow convergence, and limited ability to quantify uncertainty. This thesis presents a Bayesian framework that incorporates deep generative models, specifically a Generative Adversarial Network (GAN), to provide data-driven priors that help constrain solutions to geologically plausible structures. Variational inference techniques are applied to approximate the posterior distribution, enabling scalable inversion that accounts for uncertainty while remaining consistent with the governing physical equations. To reduce the high dimensionality of the problem, the inversion is reparameterized in the latent space of pretrained generative models, which may simplify the search space and improve convergence. A GAN-based latent reparameterization is also introduced, acting as a learned preconditioner that can accelerate optimization and reduce sensitivity to local minima. In addition, a diffusion-based Bayesian regularization strategy is proposed, where generative diffusion models are integrated directly into the FWI gradient without relying on reverse sampling, thereby avoiding instability in noisy intermediate states. Numerical experiments are used to demonstrate proof of concept, indicating that the approach may provide improved reconstructions, meaningful uncertainty estimates, and more efficient computations compared to conventional methods. Overall, the results suggest that combining generative models with Bayesian inference can offer a practical direction for advancing seismic imaging and related nonlinear inverse problems.