Generative modeling of seismic data using diffusion models and its application to multi-purpose posterior sampling for noisy inverse problems

Abstract: Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse high-quality stochastic solutions, and limits uncertainty quantification. Addressing this gap, we propose an unsupervised posterior sampling method conditioned on the noisy observations and the inverse problem, eliminating the need to retrain a task-specific conditional diffusion model with paired data for each new application. Specifically, we first propose a diffusion model enhanced with a novel noise schedule for generative modeling of seismic data, and introduce the non-Markov sampling strategy to achieve fast and quality-controllable unconditional sampling. Building upon this, we further present a posterior sampling method for various noisy inverse problems using the trained unconditional diffusion model. Our method requires only a small number of function evaluations to achieve competitive performance, while enabling flexible posterior sampling that interacts adaptively with different noise levels.Experiments on unconditional generation and posterior sampling across different tasks show that our method not only efficiently models the seismic data distribution and posterior conditioned on observations and tasks but also achieves substantially faster sampling and superior out-of-distribution generalization.