Diffusion models for multivariate subsurface generation and efficient probabilistic inversion

2025-07-21

AI Summary

This study addresses the challenge of jointly incorporating hard data (e.g., well-log facies and acoustic impedance) and nonlinear indirect geophysical data (e.g., full-waveform seismic records) in multi-variable subsurface modeling and probabilistic inversion. We propose an end-to-end conditional generative framework based on diffusion models. Methodologically, we integrate variational inference principles with denoising-based updates, designing a novel diffusion-based posterior sampling algorithm. This algorithm introduces a noise-aware likelihood approximation to enable joint conditioning on both hard data and geophysical observations, while embedding the inversion process directly into the generative sampling—eliminating the need for outer-loop iterative optimization. Compared to state-of-the-art approaches, our framework significantly improves posterior sampling efficiency and statistical robustness, achieving high-fidelity joint modeling at reduced computational cost. It establishes a scalable, high-fidelity paradigm for multi-variable subsurface uncertainty quantification.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Calibration & Uncertainty QuantificationSearch and Optimization: Sampling/Simulation-based Search

Application Category

Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphsWeb Mining and Content Analysis: Web data generation and simulationSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate that diffusion models enhance multivariate modeling capabilities compared to variational autoencoders and generative adversarial networks. In diffusion modeling, the generative process involves a comparatively large number of time steps with update rules that can be modified to account for conditioning data. We propose different corrections to the popular Diffusion Posterior Sampling approach by Chung et al. (2023). In particular, we introduce a likelihood approximation accounting for the noise-contamination that is inherent in diffusion modeling. We assess performance in a multivariate geological scenario involving facies and correlated acoustic impedance. Conditional modeling is demonstrated using both local hard data (well logs) and nonlinear geophysics (fullstack seismic data). Our tests show significantly improved statistical robustness, enhanced sampling of the posterior probability density function and reduced computational costs, compared to the original approach. The method can be used with both hard and indirect conditioning data, individually or simultaneously. As the inversion is included within the diffusion process, it is faster than other methods requiring an outer-loop around the generative model, such as Markov chain Monte Carlo.

Problem

• Enhancing multivariate subsurface modeling with diffusion models
• Improving probabilistic inversion efficiency and accuracy
• Correcting Diffusion Posterior Sampling for noise-contaminated data

Innovation

• Diffusion models enhance multivariate subsurface modeling
• Modified Diffusion Posterior Sampling with likelihood correction
• Faster inversion integrated within diffusion process