# Physics-Guided Diffusion Transformer with Spherical Harmonic Posterior Sampling for High-Fidelity Angular Super-Resolution in Diffusion MRI

arXiv: https://arxiv.org/abs/2509.07020 · HTML: https://mlsanity.com/paper/2509.07020/

## 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 17 of its 46 references that are in the map.
- First posted on arXiv 7 Sep 2025.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [MONAI: An open-source framework for deep learning in healthcare](https://mlsanity.com/paper/2211.02701/) (2022)
- [Brain Imaging Generation with Latent Diffusion Models](https://mlsanity.com/paper/2209.07162/) (2022)
- [MDTv2: Masked Diffusion Transformer is a Strong Image Synthesizer](https://mlsanity.com/paper/2303.14389/) (2023)
- [Q-space Conditioned Translation Networks for Directional Synthesis of Diffusion Weighted Images from Multi-modal Structural MRI](https://mlsanity.com/paper/2106.13188/) (2021)
- [Spatio-Angular Convolutions for Super-resolution in Diffusion MRI](https://mlsanity.com/paper/2306.00854/) (2023)
- [Diffusion MRI with Machine Learning](https://mlsanity.com/paper/2402.00019/) (2024)
- [Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes](https://mlsanity.com/paper/1706.06682/) (2017)
- [Angular Super-Resolution in Diffusion MRI with a 3D Recurrent Convolutional Autoencoder](https://mlsanity.com/paper/2203.15598/) (2022)
- [Phy-Diff: Physics-guided Hourglass Diffusion Model for Diffusion MRI Synthesis](https://mlsanity.com/paper/2406.03002/) (2024)
- [Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images](https://mlsanity.com/paper/1409.6498/) (2014)
- [Frame-wise Conditioning Adaptation for Fine-Tuning Diffusion Models in Text-to-Video Prediction](https://mlsanity.com/paper/2503.12953/) (2025)
- [Magnitude-image based data-consistent deep learning method for MRI super resolution](https://mlsanity.com/paper/2209.02901/) (2022)
- [QID2: An Image-Conditioned Diffusion Model for Q-space Up-sampling of DWI Data](https://mlsanity.com/paper/2409.02309/) (2024)

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

- [Diffusion-Encoding Gaussian Field for Joint k-q dMRI Reconstruction](https://mlsanity.com/paper/2609.02288/) (2026)

## Abstract (arXiv)

Diffusion MRI (dMRI) angular super-resolution (ASR) aims to reconstruct high-angular-resolution (HAR) signals from limited low-angular-resolution (LAR) data without prolonging scan time. However, existing methods are limited in recovering fine-grained angular details or preserving high fidelity due to inadequate modeling of q-space geometry and insufficient incorporation of physical constraints. In this paper, we introduce a Physics-Guided Diffusion Transformer (PGDiT) designed to explore physical priors throughout both training and inference stages. During training, a Q-space Geometry-Aware Module (QGAM) with b-vector modulation and random angular masking facilitates direction-aware representation learning, enabling the network to generate directionally consistent reconstructions with fine angular details from sparse and noisy data. In inference, a two-stage Spherical Harmonics-Guided Posterior Sampling (SHPS) enforces alignment with the acquired data, followed by heat-diffusion-based SH regularization to ensure physically plausible reconstructions. This coarse-to-fine refinement strategy mitigates oversmoothing and artifacts commonly observed in purely data-driven or generative models. Extensive experiments on general ASR tasks and two downstream applications, Diffusion Tensor Imaging (DTI) and Neurite Orientation Dispersion and Density Imaging (NODDI), demonstrate that PGDiT outperforms existing deep learning models in detail recovery and data fidelity. Our approach presents a novel generative ASR framework that offers high-fidelity HAR dMRI reconstructions, with potential applications in neuroscience and clinical research.