FLAT: FLow-Aligned Training of Unrolled Networks for MRI Reconstruction

Unrolled networks are widely used in Magnetic Resonance Imaging (MRI) reconstruction for their efficiency. Structured as a series of neural network stages (or cascades), an unrolled network takes a low-quality input and passes it sequentially through each stage to iteratively refine the reconstruction. However, unrolled networks 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 show that unrolled networks can be viewed as discretizations of approximate 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.