# Highly Accelerated MRI via Implicit Neural Representation Guided Posterior Sampling of Diffusion Models

arXiv: https://arxiv.org/abs/2407.02744 · HTML: https://mlsanity.com/paper/2407.02744/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 39 of its 61 references that are in the map.
- First posted on arXiv 3 Jul 2024.

## Placed in

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

## Builds on (most cited first, 30 of 39)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [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)
- [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)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [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)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [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)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [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)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [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)
- [ReconFormer: Accelerated MRI Reconstruction Using Recurrent Transformer](https://mlsanity.com/paper/2201.09376/) (2022)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models](https://mlsanity.com/paper/2202.01479/) (2022)

## Built on by (most cited first, 5 of 5)

- [SpINR: Neural Volumetric Reconstruction for FMCW Radars](https://mlsanity.com/paper/2503.23313/) (2025)
- [I-INR: Iterative Implicit Neural Representations](https://mlsanity.com/paper/2504.17364/) (2025)
- [Highly Undersampled MRI Reconstruction via a Single Posterior Sampling of Diffusion Models](https://mlsanity.com/paper/2505.08142/) (2025)
- [SpINRv2: Implicit Neural Representation for Passband FMCW Radars](https://mlsanity.com/paper/2506.08163/) (2025)
- [DiffNR: Diffusion-Enhanced Neural Representation Optimization for Sparse-View 3D Tomographic Reconstruction](https://mlsanity.com/paper/2604.21518/) (2026)

## Abstract (arXiv)

Reconstructing high-fidelity magnetic resonance (MR) images from under-sampled k-space is a commonly used strategy to reduce scan time. The posterior sampling of diffusion models based on the real measurement data holds significant promise of improved reconstruction accuracy. However, traditional posterior sampling methods often lack effective data consistency guidance, leading to inaccurate and unstable reconstructions. Implicit neural representation (INR) has emerged as a powerful paradigm for solving inverse problems by modeling a signal's attributes as a continuous function of spatial coordinates. In this study, we present a novel posterior sampler for diffusion models using INR, named DiffINR. The INR-based component incorporates both the diffusion prior distribution and the MRI physical model to ensure high data fidelity. DiffINR demonstrates superior performance on experimental datasets with remarkable accuracy, even under high acceleration factors (up to R=12 in single-channel reconstruction). Notably, our proposed framework can be a generalizable framework to solve inverse problems in other medical imaging tasks.