Learned Diffusion Model Regularization for Full Waveform Inversion

ABSTRACT The diffusion model (DM) is a class of deep generative frameworks that learn the distribution of complex data by iteratively denoising from stochastic perturbations. Here, we introduce a DM‐based regularization strategy for full‐waveform inversion (FWI), named DM‐FWI, which leverages knowledge embedded in an extensive collection of geologic velocity models to train a generalizable model for applying geological priors in a seamless manner. DM's ability to capture high‐dimensional structures and generate geologically plausible samples makes it a powerful prior for inverse problems. Within FWI, the DM serves as a structure‐adapted smoother, guiding updates towards solutions consistent with realistic geologic patterns. This implicit regularization improves the geological significance of recovered velocity models while alleviating common cycle‐skipping issues. Synthetic and field data experiments demonstrate that DM‐FWI stabilizes inversion, enhances convergence and yields subsurface models that are both quantitatively accurate and geologically interpretable.