Diffusion-guided optimization for full waveform inversion

We present a diffusion-guided full waveform inversion (FWI) study in which pretrained diffusion generative models are used as learned regularizers inside a PDE-constrained seismic inversion loop. We compare three training-free guidance strategies: Manifold-Preserving Guided Diffusion (MPGD), SDEdit-based initialization, and Split Gibbs Diffusion Sampling (SGDS), which alternates between FWI likelihood updates and diffusion-prior denoising. The proposed workflow keeps wave-equation modeling in the inversion loop and uses a geological prior to stabilize model components that are weakly constrained by the seismic data. Controlled GeoFWI experiments, benchmark-scale Marmousi and Overthrust tests, a difficult Sigsbee2A salt test, and noise-degradation studies show that SGDS improves reconstruction quality relative to conventional L2 and total-variation regularized FWI in clean and moderately noisy synthetic settings. Overall, these experiments demonstrate that diffusion-guided optimization can serve as a practical learned regularization strategy for synthetic FWI benchmarks while preserving the wave-equation modeling loop.