Accelerating Bayesian full waveform inversion using reconstruction-guided diffusion sampling

SUMMARY Full waveform inversion (FWI) is a powerful tool in seismic imaging, capable of producing high-resolution models of the subsurface. However, the method remains computationally intensive and sensitive to initial models due to its nonlinearity and ill-posed nature. To quantify uncertainty in FWI results, variational inference (VI) methods, such as Stein Variational Gradient Descent (SVGD), have been increasingly explored. These approaches approximate the posterior distribution by evolving a set of particles using gradient information from the log-posterior. Despite their promise, their effectiveness heavily depends on the quality of the prior used for initialization. In this work, we propose a hybrid framework that improves the efficiency and robustness of VI-based FWI by initializing SVGD with samples drawn from a reconstruction-guided diffusion model. Rather than replacing SVGD with a generative sampler, our approach preserves the theoretical foundations of VI while leveraging the expressive capacity of deep generative models. The diffusion model is trained to generate geologically plausible models conditioned on seismic images, thereby guiding the SVGD initialization toward regions of high posterior support. This initialization significantly reduces the number of required SVGD updates and improves convergence, while keeping the core VI formulation intact. Our results show enhanced posterior approximation and more geologically consistent solutions, with an order of magnitude lower computational cost compared to naïvely initialized SVGD. However, challenges remain, such as the computational demands of likelihood evaluations, the formation of a training set that encompasses all plausible realizations and sensitivity to reconstruction-guidance weights during sampling. Overall, this method provides a principled and efficient approach to uncertainty-aware FWI, integrating physics-informed inference with data-driven generative modelling for practical applications in full waveform inversion.