Subspace diffusion posterior sampling for travel-time tomography

Abstract Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical solvers for gradient updates. Although diffusion-based sampling methods can produce high-quality reconstructions, challenges persist in nonlinear PDE-based inverse problems and sampling speed. In this work, we explore solving PDE-based travel-time tomography based on subspace diffusion generative models. Our main contributions are twofold: first, we propose a posterior sampling process for PDE-based inverse problems by solving the associated adjoint-state equation in a plug-and-play fashion. Second, we present a subspace-based dimension reduction technique, enabling solving PDE-based inverse problems from coarse to refined grids, for conditional sampling acceleration. Our numerical experiments showed satisfactory advancements in improving the travel-time imaging quality and reducing the sampling time for reconstruction.