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

Abstract: 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.