Unrolled Networks are Conditional Probability Flows in MRI Reconstruction

Unrolled networks have been widely used for Magnetic Resonance Imaging (MRI) reconstruction due to their efficiency. However, they typically exhibit unstable output quality across cascades, resulting in sub-optimal final reconstruction results. In this work, we address this inherent limitation of unrolled networks, drawing inspiration from recent Flow Matching paradigm. We first theoretically prove that unrolled networks are discretizations of conditional probability flows. This connection shows that unrolled networks and Flow Matching are analogous in MRI reconstruction. Building upon this insight, we propose FLow-Aligned Training (FLAT), which (1) derives important cascade parameters from the Flow Matching discretization; and (2) aligns intermediate reconstructions with the ideal Flow Matching trajectory to improve cascade iteration stability and convergence. Experiments on three MRI datasets show that FLAT results in a stable trajectory across sub-networks, improving the quality of the final reconstruction.