Physics-Informed Continuous Flow Framework for Quantitative Susceptibility Mapping in MRI

The ill-posed nature of dipole inversion in Quantitative Susceptibility Mapping (QSM) introduces severe streaking artifacts. To overcome this, we present MagicFlow-QSM, a physics-guided continuous flow matching framework that reframes dipole inversion as a deterministic generative process. Rather than sampling from random noise, our method constructs a straight-line probability flow trajectory that maps a task-relevant but degraded initialization directly to a high-fidelity susceptibility target. To learn this velocity field, we parameterize a 3D U-Net target predictor trained exclusively on a simulated dataset of synthetic multi-gradient-echo brain volumes, demonstrating how targeted synthetic data generation can effectively capture complex biophysical inversion mappings without relying on paired in vivo ground truth. During inference, an ordinary differential equation (ODE) solver traverses this trajectory while dynamically enforcing physical data consistency at each sampling step using a time-decaying analytical gradient. Evaluated on clinical scans exhibiting severe field distortions from superficial siderosis (chronic bleeding), MagicFlow-QSM effectively learns to invert the physical streaking process. The proposed framework outperforms traditional optimization, neural network regularization, and baseline generative methods by at least 1.9 dB in PSNR and 2.8 ppb in MAE.