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A conditional denoising diffusion probabilistic model for continuous subsurface property modeling
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DOI：10.1016/j.cageo.2026.106260.png)
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Abstract
En 中文
Geostatistical modeling is widely recognized as a robust approach for simulating spatial variability and quantifying uncertainty in subsurface systems. As geological heterogeneity and data integration challenges increase, generative artificial intelligence (GenAI) methods are receiving growing attention for subsurface modeling. A novel generative conditional denoising diffusion probabilistic model (DDPM) is formulated for the simulation of continuous subsurface properties on regular grids. Conditioning on observed values and spatial continuity is achieved by concatenating the hard data values and their binary masks as auxiliary channels to a U-Net denoiser, and by embedding variogram descriptors (azimuth, range, anisotropy ratio, and nugget) that are injected throughout the network. A composite loss function is employed, in which the standard noise prediction objective is augmented with a hard data term that promotes exact reproduction of conditioning values while the target spatial continuity is preserved. The DDPM is trained and evaluated on continuous Gaussian data, which provide a controlled benchmark for developing and assessing the proposed conditional framework. Numerical experiments across multiple test cases, both within and outside the training domain, show that the conditional DDPM reproduces histograms and variograms, provides local uncertainty estimates comparable to those of simple kriging, and captures the global variability of reference ensembles, as assessed by multidimensional scaling and coverage analyses. These results indicate that the conditional DDPM can provide a flexible GenAI based framework for continuous subsurface modeling.
Keywords:
Generative artificial intelligence
Conditional subsurface modeling
Denoising diffusion probabilistic models
Hard data conditioning
Variogram embedding
Continuous property simulation
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4.4
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103
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