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

arXiv: https://arxiv.org/abs/2511.16926 · HTML: https://mlsanity.com/paper/2511.16926/

## 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.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 12 of 12)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Large Scale Structure of Neural Network Loss Landscapes](https://mlsanity.com/paper/1906.04724/) (2019)
- [Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media](https://mlsanity.com/paper/1807.00882/) (2018)
- [A Fourier Space Perspective on Diffusion Models](https://mlsanity.com/paper/2505.11278/) (2025)
- [Training-image based geostatistical inversion using a spatial generative adversarial neural network](https://mlsanity.com/paper/1708.04975/) (2017)
- [Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Example](https://mlsanity.com/paper/2007.15580/) (2020)
- [Discovering state-parameter mappings in subsurface models using generative adversarial networks](https://mlsanity.com/paper/1810.12856/) (2018)

## 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.