Geological Inverse Problem‐Solving Method Based on Diffusion Models

Abstract

Traditional geological parameter inversion methods often require repeated forward simulations for history matching, leading to high computational cost and limited inversion efficiency. Their performance may also be restricted when geological fields exhibit strong non‐Gaussian characteristics. To address these challenges, this study proposes an end‐to‐end inversion modeling workflow, termed DDPM‐DSI, which integrates a Denoising Diffusion Probabilistic Model (DDPM) with Data‐Space Inversion (DSI). In the proposed workflow, a probabilistic sparse attention encoder is used to extract temporal features from multivariate production data and provide conditioning information for the diffusion model. Geological parameter fields are represented in a reduced latent space using Principal Component Analysis (PCA) for Gaussian‐like cases and a Vector‐Quantized Variational Autoencoder (VQ‐VAE) for channelized non‐Gaussian cases. The DSI method is then applied to generate posterior dynamic‐response samples from observed data and prior simulations, which are used to condition the trained diffusion model for direct generation of posterior geological parameter fields. The proposed workflow is evaluated using a 2D synthetic reservoir model, a 3D Brugge benchmark model, and a non‐Gaussian Egg benchmark model. The results show that DDPM‐DSI can recover major geological structures and reproduce production‐response trends in the tested cases. Compared with traditional GAN‐based inversion, DDPM‐DSI generally produces sharper and more geologically consistent posterior realizations, particularly for non‐Gaussian channelized fields. Compared with the Ensemble Smoother with Multiple Data Assimilation (ESMDA), DDPM‐DSI provides rapid online inference after problem‐specific training and avoids repeated simulator‐based parameter updates during inversion. These results indicate that DDPM‐DSI provides a promising generative inversion framework for efficient history matching and geological parameter estimation under complex geological conditions.