# SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI arXiv: https://arxiv.org/abs/2304.05060 ยท HTML: https://mlsanity.com/paper/2304.05060/ ## Key facts - Cited by 12 papers in the map (data through 14 Oct 2026). - Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models. - Builds on 22 of its 50 references that are in the map. - First posted on arXiv 11 Apr 2023. ## Placed in - Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/) ## Builds on (most cited first, 22 of 22) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019) - [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020) - [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019) - [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022) - [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020) - [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021) - [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018) - [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017) - [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022) - [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021) - [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021) - [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017) - [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023) - [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022) - [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) - [High-Frequency Space Diffusion Models for Accelerated MRI](https://mlsanity.com/paper/2208.05481/) (2022) - [Deep Generalization of Structured Low-Rank Algorithms (Deep-SLR)](https://mlsanity.com/paper/1912.03433/) (2019) - [LORAKI: Autocalibrated Recurrent Neural Networks for Autoregressive MRI Reconstruction in k-Space](https://mlsanity.com/paper/1904.09390/) (2019) - [Navigator-free EPI Ghost Correction with Structured Low-Rank Matrix Models: New Theory and Methods](https://mlsanity.com/paper/1708.05095/) (2017) - [Estimating Absolute-Phase Maps Using ESPIRiT and Virtual Conjugate Coils](https://mlsanity.com/paper/1509.03557/) (2015) ## Built on by (most cited first, 12 of 12) - [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023) - [Correlated and Multi-frequency Diffusion Modeling for Highly Under-sampled MRI Reconstruction](https://mlsanity.com/paper/2309.00853/) (2023) - [A Survey of Emerging Applications of Diffusion Probabilistic Models in MRI](https://mlsanity.com/paper/2311.11383/) (2023) - [Denoising Diffusion Probabilistic Models for Magnetic Resonance Fingerprinting](https://mlsanity.com/paper/2410.23318/) (2024) - [Meta-Learning Enabled Score-Based Generative Model for 1.5T-Like Image Reconstruction from 0.5T MRI](https://mlsanity.com/paper/2305.02509/) (2023) - [Highly Undersampled MRI Reconstruction via a Single Posterior Sampling of Diffusion Models](https://mlsanity.com/paper/2505.08142/) (2025) - [JSMoCo: Joint Coil Sensitivity and Motion Correction in Parallel MRI with a Self-Calibrating Score-Based Diffusion Model](https://mlsanity.com/paper/2310.09625/) (2023) - [Diffusion assisted image reconstruction in optoacoustic tomography](https://mlsanity.com/paper/2404.10239/) (2024) - [Guided MRI Reconstruction via Schr"odinger Bridge](https://mlsanity.com/paper/2411.14269/) (2024) - [Learning the Domain Specific Inverse NUFFT for Accelerated Spiral MRI using Diffusion Models](https://mlsanity.com/paper/2404.12361/) (2024) - [Measured-Subspace Consistency: A Plug-and-Play Operator for Diffusion Posterior Sampling in Accelerated MRI Reconstruction](https://mlsanity.com/paper/2606.28448/) (2026) - [Self-Auditing Residual Drifting for Pathology-Preserving Accelerated Knee MRI](https://mlsanity.com/paper/2607.02428/) (2026) ## Abstract (arXiv) Diffusion models have emerged as a leading methodology for image generation and have proven successful in the realm of magnetic resonance imaging (MRI) reconstruction. However, existing reconstruction methods based on diffusion models are primarily formulated in the image domain, making the reconstruction quality susceptible to inaccuracies in coil sensitivity maps (CSMs). k-space interpolation methods can effectively address this issue but conventional diffusion models are not readily applicable in k-space interpolation. To overcome this challenge, we introduce a novel approach called SPIRiT-Diffusion, which is a diffusion model for k-space interpolation inspired by the iterative self-consistent SPIRiT method. Specifically, we utilize the iterative solver of the self-consistent term (i.e., k-space physical prior) in SPIRiT to formulate a novel stochastic differential equation (SDE) governing the diffusion process. Subsequently, k-space data can be interpolated by executing the diffusion process. This innovative approach highlights the optimization model's role in designing the SDE in diffusion models, enabling the diffusion process to align closely with the physics inherent in the optimization model, a concept referred to as model-driven diffusion. We evaluated the proposed SPIRiT-Diffusion method using a 3D joint intracranial and carotid vessel wall imaging dataset. The results convincingly demonstrate its superiority over image-domain reconstruction methods, achieving high reconstruction quality even at a substantial acceleration rate of 10.