Two-Parameter Flow Map Learning for Continuous-Time Diffeomorphic Image Registration

Learning-based medical image registration has matched the accuracy of conventional methods while offering superior computational efficiency. However, existing approaches suffer from poor generalization across diverse clinical scenarios, requiring the laborious development of multiple isolated networks for specific registration tasks, \emph{e.g.}, inter-/intra-subject registration or anatomical region-specific alignment, leading to cumbersome development pipelines. To overcome this limitation, we propose \textbf{UniReg}, the first conditional unified model for multi-scenario medical image registration, which combines the precision advantages of task-specific learning methods with the generalization of traditional optimization methods. Our key innovation is a unified registration framework that adaptively estimates deformation fields conditioned on: (1) anatomical structure priors, (2) registration type constraints (inter/intra-subject), and (3) instance-specific features, enabling effective alignment across heterogeneous CT and MR registration scenarios within a single model. Through comprehensive experiments on multiple CT/MR registration datasets, UniReg achieves superior average registration accuracy compared with current state-of-the-art learning-based methods while exhibiting strong cross-scenario generalization. Moreover, by replacing multiple isolated task-specific models with a compact unified model, UniReg substantially reduces the overall training burden in terms of total training cost and model redundancy.

Medical image registration benefits significantly from deep learning, yet existing approaches often lack physical explainability and fine-grained deformation control. Motivated by Demons algorithms, we propose a novel DrivenMorph framework that bridges attention mechanisms with variational image registration by incorporating difference modeling as a physically inspired inductive bias. The resulting driving force, computed from local differences in the latent feature space, provides explicit semantic guidance throughout the registration process. It directly drives the registration process through a neural Demons layer that simulates force-displacement interactions to generate smooth and anatomically consistent deformation. Unlike previous methods, our approach not only integrates traditional registration principles with popular deep networks, providing an explainable and efficient solution for learning-based medical image registration, but also separates difference modeling from deformation, improving modularity and explainability. Extensive experiments on multiple 3D brain MRI datasets demonstrate superior performance over state of-the-art learning-based and optimization-based methods. Furthermore, visualizations and statistical analyses confirm that the learned driving force aligns closely with actual deformation patterns, supporting its explanatory value.

Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration. Consistency models address this by directly learning the flow maps along the ODE trajectory, opening a design space between one-step and many-step approaches. However, existing methods face computational challenges such as requiring model inverses or backpropagation through iterated model calls, and do not always prove that the desired ODE flow map is a solution to the loss. We introduce SGFlow, an approach for learning flow maps that bypasses explicit invertibility constraints and expensive differentiation through model iteration. SGFlow trains a model to compute both the ODE solutions and the implied velocity from scratch by following non-conservative dynamics with a stationary point at the desired flow map. On the CIFAR image benchmark, no single method attains the best FID at every step count: SGFlow attains the best FID at 10 sampling steps and remains competitive with flow matching, Meanflow, and Lagrangian map matching at other step counts, while being the only one with a proven stationary-point guarantee for its stopgrad-based dynamics.