# Solving 3D Inverse Problems using Pre-trained 2D Diffusion Models

arXiv: https://arxiv.org/abs/2211.10655 · HTML: https://mlsanity.com/paper/2211.10655/

## Key facts

- Cited by 132 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 25 of its 40 references that are in the map.
- First posted on arXiv 19 Nov 2022.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Brain Imaging Generation with Latent Diffusion Models](https://mlsanity.com/paper/2209.07162/) (2022)
- [A Conditional Point Diffusion-Refinement Paradigm for 3D Point Cloud Completion](https://mlsanity.com/paper/2112.03530/) (2021)
- [A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstruction](https://mlsanity.com/paper/1610.09736/) (2016)
- [DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Prior](https://mlsanity.com/paper/2001.03799/) (2020)
- [A Diffusion Model Predicts 3D Shapes from 2D Microscopy Images](https://mlsanity.com/paper/2208.14125/) (2022)
- [Sparse-view Cone Beam CT Reconstruction using Data-consistent Supervised and Adversarial Learning from Scarce Training Data](https://mlsanity.com/paper/2201.09318/) (2022)
- [Image Prediction for Limited-angle Tomography via Deep Learning with Convolutional Neural Network](https://mlsanity.com/paper/1607.08707/) (2016)

## Built on by (most cited first, 30 of 132)

- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [Structure-Aware Sparse-View X-ray 3D Reconstruction](https://mlsanity.com/paper/2311.10959/) (2023)
- [Prompt-tuning latent diffusion models for inverse problems](https://mlsanity.com/paper/2310.01110/) (2023)
- [R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction](https://mlsanity.com/paper/2405.20693/) (2024)
- [Direct Diffusion Bridge using Data Consistency for Inverse Problems](https://mlsanity.com/paper/2305.19809/) (2023)
- [Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Models](https://mlsanity.com/paper/2303.08440/) (2023)
- [CoreDiff: Contextual Error-Modulated Generalized Diffusion Model for Low-Dose CT Denoising and Generalization](https://mlsanity.com/paper/2304.01814/) (2023)
- [Make-A-Volume: Leveraging Latent Diffusion Models for Cross-Modality 3D Brain MRI Synthesis](https://mlsanity.com/paper/2307.10094/) (2023)
- [GSURE-Based Diffusion Model Training with Corrupted Data](https://mlsanity.com/paper/2305.13128/) (2023)
- [Regularization by Texts for Latent Diffusion Inverse Solvers](https://mlsanity.com/paper/2311.15658/) (2023)
- [DyMO: Training-Free Diffusion Model Alignment with Dynamic Multi-Objective Scheduling](https://mlsanity.com/paper/2412.00759/) (2024)
- [3DGR-CT: Sparse-View CT Reconstruction with a 3D Gaussian Representation](https://mlsanity.com/paper/2312.15676/) (2023)
- [Score-Based Generative Models for PET Image Reconstruction](https://mlsanity.com/paper/2308.14190/) (2023)
- [Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problems](https://mlsanity.com/paper/2407.10641/) (2024)
- [Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problems](https://mlsanity.com/paper/2406.02462/) (2024)
- [DPER: Diffusion Prior Driven Neural Representation for Limited Angle and Sparse View CT Reconstruction](https://mlsanity.com/paper/2404.17890/) (2024)
- [SMRD: SURE-based Robust MRI Reconstruction with Diffusion Models](https://mlsanity.com/paper/2310.01799/) (2023)
- [Diffusion models for inverse problems](https://mlsanity.com/paper/2508.01975/) (2025)
- [Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstruction](https://mlsanity.com/paper/2308.14409/) (2023)
- [C^2RV: Cross-Regional and Cross-View Learning for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2406.03902/) (2024)
- [Solving Video Inverse Problems Using Image Diffusion Models](https://mlsanity.com/paper/2409.02574/) (2024)
- [Deep Generative Models for 3D Medical Image Synthesis](https://mlsanity.com/paper/2410.17664/) (2024)
- [A 3D Conditional Diffusion Model for Image Quality Transfer -- An Application to Low-Field MRI](https://mlsanity.com/paper/2311.06631/) (2023)
- [Learning to Compose: Improving Object Centric Learning by Injecting Compositionality](https://mlsanity.com/paper/2405.00646/) (2024)
- [2.5D Multi-view Averaging Diffusion Model for 3D Medical Image Translation: Application to Low-count PET Reconstruction with CT-less Attenuation Correction](https://mlsanity.com/paper/2406.08374/) (2024)
- [DiffusionBlend: Learning 3D Image Prior through Position-aware Diffusion Score Blending for 3D Computed Tomography Reconstruction](https://mlsanity.com/paper/2406.10211/) (2024)
- [Geometry-Aware Attenuation Learning for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2303.14739/) (2023)

## Abstract (arXiv)

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers, acting as the prior of the distribution, while the information of the forward model can be granted at the sampling stage. Nonetheless, as the generative process remains in the same high dimensional (i.e. identical to data dimension) space, the models have not been extended to 3D inverse problems due to the extremely high memory and computational cost. In this paper, we combine the ideas from the conventional model-based iterative reconstruction with the modern diffusion models, which leads to a highly effective method for solving 3D medical image reconstruction tasks such as sparse-view tomography, limited angle tomography, compressed sensing MRI from pre-trained 2D diffusion models. In essence, we propose to augment the 2D diffusion prior with a model-based prior in the remaining direction at test time, such that one can achieve coherent reconstructions across all dimensions. Our method can be run in a single commodity GPU, and establishes the new state-of-the-art, showing that the proposed method can perform reconstructions of high fidelity and accuracy even in the most extreme cases (e.g. 2-view 3D tomography). We further reveal that the generalization capacity of the proposed method is surprisingly high, and can be used to reconstruct volumes that are entirely different from the training dataset.