# A Flow-based Truncated Denoising Diffusion Model for Super-resolution Magnetic Resonance Spectroscopic Imaging

arXiv: https://arxiv.org/abs/2410.19288 · HTML: https://mlsanity.com/paper/2410.19288/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 24 of its 52 references that are in the map.
- First posted on arXiv 25 Oct 2024.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescaling](https://mlsanity.com/paper/2108.05301/) (2021)
- [Towards performant and reliable undersampled MR reconstruction via diffusion model sampling](https://mlsanity.com/paper/2203.04292/) (2022)
- [Invertible Sharpening Network for MRI Reconstruction Enhancement](https://mlsanity.com/paper/2206.02838/) (2022)
- [Multi-scale Super-resolution Magnetic Resonance Spectroscopic Imaging with Adjustable Sharpness](https://mlsanity.com/paper/2206.08984/) (2022)
- [Flow-based Visual Quality Enhancer for Super-resolution Magnetic Resonance Spectroscopic Imaging](https://mlsanity.com/paper/2207.10181/) (2022)
- [Preserved Edge Convolutional Neural Network for Sensitivity Enhancement of Deuterium Metabolic Imaging (DMI)](https://mlsanity.com/paper/2309.04100/) (2023)

## Built on by (most cited first, 2 of 2)

- [MRI Super-Resolution with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2511.16854/) (2025)
- [Extendable Generalization Self-Supervised Diffusion for Low-Dose CT Reconstruction](https://mlsanity.com/paper/2509.23885/) (2025)

## Abstract (arXiv)

Magnetic Resonance Spectroscopic Imaging (MRSI) is a non-invasive imaging technique for studying metabolism and has become a crucial tool for understanding neurological diseases, cancers and diabetes. High spatial resolution MRSI is needed to characterize lesions, but in practice MRSI is acquired at low resolution due to time and sensitivity restrictions caused by the low metabolite concentrations. Therefore, there is an imperative need for a post-processing approach to generate high-resolution MRSI from low-resolution data that can be acquired fast and with high sensitivity. Deep learning-based super-resolution methods provided promising results for improving the spatial resolution of MRSI, but they still have limited capability to generate accurate and high-quality images. Recently, diffusion models have demonstrated superior learning capability than other generative models in various tasks, but sampling from diffusion models requires iterating through a large number of diffusion steps, which is time-consuming. This work introduces a Flow-based Truncated Denoising Diffusion Model (FTDDM) for super-resolution MRSI, which shortens the diffusion process by truncating the diffusion chain, and the truncated steps are estimated using a normalizing flow-based network. The network is conditioned on upscaling factors to enable multi-scale super-resolution. To train and evaluate the deep learning models, we developed a 1H-MRSI dataset acquired from 25 high-grade glioma patients. We demonstrate that FTDDM outperforms existing generative models while speeding up the sampling process by over 9-fold compared to the baseline diffusion model. Neuroradiologists' evaluations confirmed the clinical advantages of our method, which also supports uncertainty estimation and sharpness adjustment, extending its potential clinical applications.