Diffusion prior as a direct regularization term for FWI

Diffusion models have recently shown promise as powerful generative priors for inverse problems. However, conventional applications require solving the full reverse diffusion process and operating on noisy intermediate states, which poses challenges for physics-constrained computational seismic imaging. In particular, such instability is pronounced in non-linear solvers like those used in Full Waveform Inversion (FWI), where wave propagation through noisy velocity fields can lead to numerical artifacts and poor inversion quality. In this work, we propose a simple yet effective framework that directly integrates a pretrained Denoising Diffusion Probabilistic Model (DDPM) as a score-based generative diffusion prior into FWI through a score rematching strategy. Unlike traditional diffusion approaches, our method avoids the reverse diffusion sampling and needs fewer iterations. We operate the image inversion entirely in the clean image space, eliminating the need to operate through noisy velocity models. The generative diffusion prior can be introduced as a simple regularization term in the standard FWI update rule, requiring minimal modification to existing FWI pipelines. This promotes stable wave propagation and can improve convergence behavior and inversion quality. Numerical experiments suggest that the proposed method offers enhanced fidelity and robustness compared to conventional and GAN-based FWI approaches, while remaining practical and computationally efficient for seismic imaging and other inverse problem tasks.