mlsanityData to 14 Oct 2026

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

arXiv 2511.16926 ↗First posted 21 Nov 2025physics.geo-ph stat.MLcited by 0

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 12 of its 36 references that are in the map. First posted on arXiv 21 Nov 2025.

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12 of 36 references.

References · 12

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  5. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,333
  6. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,114
  7. 2019Large Scale Structure of Neural Network Loss Landscapescited by 68
  8. 2018Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous mediacited by 56
  9. 2025A Fourier Space Perspective on Diffusion Modelscited by 52
  10. 2017Training-image based geostatistical inversion using a spatial generative adversarial neural networkcited by 32
  11. 2020Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Examplecited by 13
  12. 2018Discovering state-parameter mappings in subsurface models using generative adversarial networkscited by 7

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  4. 2025Differentiable Inverse Modeling with Physics-Constrained Latent Diffusion for Heterogeneous Subsurface Parameter Fields
  5. 2026Data assimilation for subsurface flow using latent diffusion model parameterization: performance of ensemble-Kalman and Monte Carlo techniques
  6. 2025Diffusion models for multivariate subsurface generation and efficient probabilistic inversion
  7. 2026Function-Space Decoupled Diffusion for Forward and Inverse Modeling in Carbon Capture and Storage
  8. 2026Beyond Accuracy: Evaluating Posterior Fidelity of Diffusion Inverse Solvers