# CT Reconstruction using Diffusion Posterior Sampling conditioned on a Nonlinear Measurement Model

arXiv: https://arxiv.org/abs/2312.01464 · HTML: https://mlsanity.com/paper/2312.01464/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 3 Dec 2023.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Diffusion Probabilistic Models beat GANs on Medical Images](https://mlsanity.com/paper/2212.07501/) (2022)
- [DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction](https://mlsanity.com/paper/2211.12340/) (2022)
- [A New 2.5D Representation for Lymph Node Detection using Random Sets of Deep Convolutional Neural Network Observations](https://mlsanity.com/paper/1406.2639/) (2014)
- [Patch-Based Denoising Diffusion Probabilistic Model for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2211.10388/) (2022)
- [Differentiable Forward Projector for X-ray Computed Tomography](https://mlsanity.com/paper/2307.05801/) (2023)
- [Diffusion Prior Regularized Iterative Reconstruction for Low-dose CT](https://mlsanity.com/paper/2310.06949/) (2023)

## Built on by (most cited first, 6 of 6)

- [Physics-Inspired Generative Models in Medical Imaging: A Review](https://mlsanity.com/paper/2407.10856/) (2024)
- [CT Material Decomposition using Spectral Diffusion Posterior Sampling](https://mlsanity.com/paper/2402.03476/) (2024)
- [Strategies for CT Reconstruction using Diffusion Posterior Sampling with a Nonlinear Model](https://mlsanity.com/paper/2407.12956/) (2024)
- [MInDI-3D: Iterative Deep Learning in 3D for Sparse-view Cone Beam Computed Tomography](https://mlsanity.com/paper/2508.09616/) (2025)
- [Multilevel Stochastic Plug-and-Play for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2606.24567/) (2026)
- [Backward SDEs-based Diffusion for Physics-Constrained Generation](https://mlsanity.com/paper/2609.15702/) (2026)

## Abstract (arXiv)

Diffusion models have been demonstrated as powerful deep learning tools for image generation in CT reconstruction and restoration. Recently, diffusion posterior sampling, where a score-based diffusion prior is combined with a likelihood model, has been used to produce high quality CT images given low-quality measurements. This technique is attractive since it permits a one-time, unsupervised training of a CT prior; which can then be incorporated with an arbitrary data model. However, current methods rely on a linear model of x-ray CT physics to reconstruct or restore images. While it is common to linearize the transmission tomography reconstruction problem, this is an approximation to the true and inherently nonlinear forward model. We propose a new method that solves the inverse problem of nonlinear CT image reconstruction via diffusion posterior sampling. We implement a traditional unconditional diffusion model by training a prior score function estimator, and apply Bayes rule to combine this prior with a measurement likelihood score function derived from the nonlinear physical model to arrive at a posterior score function that can be used to sample the reverse-time diffusion process. This plug-and-play method allows incorporation of a diffusion-based prior with generalized nonlinear CT image reconstruction into multiple CT system designs with different forward models, without the need for any additional training. We develop the algorithm that performs this reconstruction, including an ordered-subsets variant for accelerated processing and demonstrate the technique in both fully sampled low dose data and sparse-view geometries using a single unsupervised training of the prior.