Flow-QSM: bridging learned priors and physical models for quantitative susceptibility mapping

Objective.Quantitative susceptibility mapping (QSM) is a magnetic resonance imaging technique that quantifies tissue magnetic susceptibility by solving an ill-posed inverse problem from measured magnetic field perturbations. Its accuracy is fundamentally limited by the non-local dipole kernel and the lack of a universally accurate and generalizable prior.Approach.We propose Flow-QSM, a physics-guided conditional flow-matching framework for efficient and accurate QSM reconstruction. The method first learns a generative prior of susceptibility maps via unconditional flow matching. It then performs a physics-guided reverse sampling process, where the generative prior is conditioned and corrected by the physical forward model through a predicted flow velocity field. This establishes a probabilistic bridge between the prior and posterior distributions, ensuring an optimal balance between data fidelity and learned anatomical constraints. Specifically, we design a customized architecture featuring (i) a patch-wise positional encoding mechanism to maintain global spatial coherence across partitioned sub-volumes, and (ii) a dual branch skip-backbone modulation strategy to adaptively fuse spatially enriched and frequency-refined features for high-fidelity detail recovery.Experiments.Comprehensive evaluations onin vivohuman brain datasets suggest that Flow-QSM achieves improved accuracy and artifact suppression compared with representative QSM reconstruction methods. Its performance is further examined on high-resolution data, clinical data, and out-of-domain cases, where it demonstrates consistent behavior while maintaining efficient inference time.Significance.Flow-QSM provides a unified probabilistic framework that integrates learned generative priors with physics-based constraints for susceptibility mapping. The proposed approach offers a flexible and principled strategy for addressing ill-posed inverse problems in computational imaging.