# Full Waveform Inversion

Full waveform inversion reconstructs subsurface velocity models from seismic records, but it is highly nonlinear and ill-posed, and an inaccurate initial model or noisy data can push it to a wrong solution. Bayesian full waveform inversion built on annealed Stein variational gradient descent previously constrained its particles with handcrafted Gaussian or smoothing priors that cannot represent complex geology. This work embeds a diffusion model trained on the GeoFWI dataset as an implicit geological projection operator inside the particle update, lowering mean absolute error on the Marmousi synthetic model from 94.80 with the classic method to 92.68, raising structural similarity from 0.69 to 0.72, and concentrating posterior uncertainty near deep structures and high-contrast interfaces.

Full waveform inversion reconstructs subsurface velocity models from seismic records, but it is highly nonlinear and ill-posed, and an inaccurate initial model or noisy data can push it to a wrong solution. Bayesian full waveform inversion built on annealed Stein variational gradient descent previously constrained its particles with handcrafted Gaussian or smoothing priors that cannot represent complex geology. This work embeds a diffusion model trained on the GeoFWI dataset as an implicit geological projection operator inside the particle update, lowering mean absolute error on the Marmousi synthetic model from 94.80 with the classic method to 92.68, raising structural similarity from 0.69 to 0.72, and concentrating posterior uncertainty near deep structures and high-contrast interfaces.