Title: Unrolled Networks are Conditional Probability Flows in MRI Reconstruction
Primary area: generative models
Keywords: Magnetic Resonance Imaging, Unrolled Networks, Conditional Probability Flow, Ordinary Differential Equations

Abstract: Magnetic Resonance Imaging (MRI) offers excellent soft-tissue contrast without ionizing radiation, but its long acquisition time limits clinical utility. Recent methods accelerate MRI by under-sampling k-space and reconstructing the resulting images using deep learning. Unrolled networks have been widely used for the reconstruction task due to their efficiency, but suffer from unstable training caused by unconstrained hyperparameters and lack of intermediate supervision. In contrast, flow ODEs based on conditional probability Ordinary Differential Equations offer theoretical stability in natural image tasks but are computationally expensive and lack MRI-specific formulations. In this work, we introduce flow ODEs to MRI reconstruction by theoretically proving that unrolled networks are discrete implementations of conditional probability flow ODEs. This connection provides explicit formulations for hyperparameters and clarifies how intermediate states should evolve. Building on this insight, we propose Flow-Aligned Training (FLAT), which derives unrolled hyperparameters from the ODE discretization and aligns intermediate reconstructions with the ideal ODE trajectory to improve stability and convergence. Experiments on three MRI datasets show that FLAT achieves high-quality reconstructions with up to 3x fewer iterations and significantly greater stability than unrolled and diffusion-based generative models.