Diffusion-Inversion-Net (DIN): An End-to-End Direct Probabilistic Framework for Characterizing Hydraulic Conductivities and Quantifying Uncertainty

TL;DR

The paper introduces DIN, a novel probabilistic framework using diffusion models for direct, end-to-end inversion of groundwater parameters, enabling accurate estimation and uncertainty quantification without iterative simulations.

Contribution

DIN is the first framework to integrate diffusion models for direct inversion of groundwater properties, bypassing traditional iterative methods and providing robust uncertainty quantification.

Findings

Accurately estimates hydraulic-conductivity fields.

Generates multiple constraint-satisfying realizations.

Demonstrates strong generalization across data types.

Abstract

We propose the Diffusion-Inversion-Net (DIN) framework for inverse modeling of groundwater flow and solute transport processes. DIN utilizes an offline-trained Denoising Diffusion Probabilistic Model (DDPM) as a powerful prior leaner, which flexibly incorporates sparse, multi-source observational data, including hydraulic head, solute concentration, and hard conductivity data, through conditional injection mechanisms. These conditioning inputs subsequently guide the generative inversion process during sampling. Bypassing iterative forward simulations, DIN leverages stochastic sampling and probabilistic modeling mechanisms to directly generate ensembles of posterior parameter fields by repeatedly executing the reverse denoising process. Two representative posterior scenarios, Gaussian and non-Gaussian, are investigated. The results demonstrate that DIN can produce multiple constraint-satisfying realizations under identical observational conditions, accurately estimate hydraulic-conductivity fields, and achieve reliable uncertainty quantification. The framework exhibits strong generalization capability across diverse data distributions, offering a robust and unified alternative to conventional multi-stage inversion methodologies.