Recent work that combines diffusion or score-based priors with EIT:
- Diff-INR (Tong, Wang, Liu 2024): represents the conductivity as an implicit neural representation and uses a pretrained diffusion model as a generative regulariser during the reconstruction.
- Conditional diffusion (Shi, Kang, Liatsis 2024): trains a diffusion model conditioned on the boundary measurements, so boundary-operator information enters the generative model directly.
- Diffusion graph posterior sampling (Alberti, Lazzaro, Morigi, Santacesaria, Wang 2026): adapts the diffusion architecture to conductivities on unstructured FEM meshes via graph networks, instead of pixel grids, for nonlinear inverse problems such as EIT.
- Comparative study (Wang, Xu, Zhou 2024): VAEs, normalising flows and score-based diffusion models as priors for EIT, within a common Bayesian framework.
Recurring themes.
- EIT’s forward operator is expensive and nonlinear. Methods that need few forward solves or tolerate inexact data steps (DiffPIR, RED-Diff) are more practical than those that backpropagate through the network at every step (Diffusion Posterior Sampling).
- Pixel-grid diffusion models do not match FEM meshes or curved domains. Mask channels, conformal maps to a reference domain or graph networks on the mesh bridge the gap (see U-Net and Networks on EIT Domains).
- Weakly determined interiors invite hallucinations. Multiple posterior samples are the natural uncertainty estimate.
References
- B. Tong, J. Wang, D. Liu (2024). Diff-INR: Generative Regularization for Electrical Impedance Tomography. arXiv:2409.04494
- S. Shi, R. Kang, P. Liatsis (2024). A Conditional Diffusion Model for Electrical Impedance Tomography Image Reconstruction. arXiv:2412.16979
- G. S. Alberti, D. Lazzaro, S. Morigi, M. Santacesaria, S. Wang (2026). Diffusion Graph Posterior Sampling for Nonlinear Inverse Problems with Application to Electrical Impedance Tomography. arXiv:2605.19621
- H. Wang, G. Xu, Q. Zhou (2024). A Comparative Study of Variational Autoencoders, Normalizing Flows, and Score-based Diffusion Models for Electrical Impedance Tomography. arXiv:2310.15831