G ² IFWI: Gradient‐Coupled Diffusion Priors for Regularizing Implicit Full Waveform Inversion

Abstract

Full waveform inversion (FWI) aims to recover high‐resolution subsurface velocity models but remains highly ill‐posed due to strong nonlinearity, cycle‐skipping, and solution non‐uniqueness. Implicit neural representations (INRs) with multiresolution hash encoding provide an efficient continuous parameterization for implicit FWI (IFWI). However, IFWI can still produce geologically unrealistic structures and spurious high‐frequency artifacts. We propose a learned regularization framework that integrates a denoising diffusion probabilistic model (DDPM) into multiresolution hash encoding‐based IFWI, as a Gradient‐Coupled Diffusion Prior for IFWI (IFWI). The inversion is guided by the joint optimization of the physics‐based IFWI gradient and the score gradient derived from the diffusion prior. If available, well‐log measurements are further imposed through guidance to anchor the inversion locally. Experiments on both synthetic examples and a challenging short‐offset field data set demonstrate that the proposed framework improves inversion stability, suppresses artificial high‐frequency features, and enhances reconstruction accuracy.