# Self-Consistent Nested Diffusion Bridge for Accelerated MRI Reconstruction

arXiv: https://arxiv.org/abs/2412.09998 · HTML: https://mlsanity.com/paper/2412.09998/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 21 of its 43 references that are in the map.
- First posted on arXiv 13 Dec 2024.

## Placed in

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

## Builds on (most cited first, 21 of 21)

- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [BBDM: Image-to-image Translation with Brownian Bridge Diffusion Models](https://mlsanity.com/paper/2205.07680/) (2022)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Direct Diffusion Bridge using Data Consistency for Inverse Problems](https://mlsanity.com/paper/2305.19809/) (2023)
- [Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstruction](https://mlsanity.com/paper/2203.03623/) (2022)
- [Towards performant and reliable undersampled MR reconstruction via diffusion model sampling](https://mlsanity.com/paper/2203.04292/) (2022)
- [GrappaNet: Combining Parallel Imaging with Deep Learning for Multi-Coil MRI Reconstruction](https://mlsanity.com/paper/1910.12325/) (2019)
- [High-Frequency Space Diffusion Models for Accelerated MRI](https://mlsanity.com/paper/2208.05481/) (2022)
- [Self-Consistent Recursive Diffusion Bridge for Medical Image Translation](https://mlsanity.com/paper/2405.06789/) (2024)
- [Unsupervised MRI Reconstruction with Generative Adversarial Networks](https://mlsanity.com/paper/2008.13065/) (2020)
- [Data augmentation for deep learning based accelerated MRI reconstruction with limited data](https://mlsanity.com/paper/2106.14947/) (2021)
- [Equilibrated Zeroth-Order Unrolled Deep Networks for Accelerated MRI](https://mlsanity.com/paper/2112.09891/) (2021)

## Built on by (most cited first, 1 of 1)

- [Conditional Denoising Diffusion Model-Based Robust MR Image Reconstruction from Highly Undersampled Data](https://mlsanity.com/paper/2510.06335/) (2025)

## Abstract (arXiv)

Accelerated MRI reconstruction plays a vital role in reducing scan time while preserving image quality. While most existing methods rely on complex-valued image-space or k-space data, these formats are often inaccessible in clinical practice due to proprietary reconstruction pipelines, leaving only magnitude images stored in DICOM files. To address this gap, we focus on the underexplored task of magnitude-image-based MRI reconstruction. Recent advancements in diffusion models, particularly denoising diffusion probabilistic models (DDPMs), have demonstrated strong capabilities in modeling image priors. However, their task-agnostic denoising nature limits performance in source-to-target image translation tasks, such as MRI reconstruction. In this work, we propose a novel Self-Consistent Nested Diffusion Bridge (SC-NDB) framework that models accelerated MRI reconstruction as a bi-directional image translation process between under-sampled and fully-sampled magnitude MRI images. SC-NDB introduces a nested diffusion architecture with a self-consistency constraint and reverse bridge diffusion pathways to improve intermediate prediction fidelity and better capture the explicit priors of source images. Furthermore, we incorporate a Contour Decomposition Embedding Module (CDEM) to inject structural and textural knowledge by leveraging Laplacian pyramids and directional filter banks. Extensive experiments on the fastMRI and IXI datasets demonstrate that our method achieves state-of-the-art performance compared to both magnitude-based and non-magnitude-based diffusion models, confirming the effectiveness and clinical relevance of SC-NDB.