FlowCycle: Rethinking Cycle Consistency via Exact Bijective Latent Flows

Bidirectional cross-modal translation often entails a compromise between inference efficiency and formal invertibility. Continuous diffusion-based approaches typically require computationally intensive ordinary differential equation (ODE) solvers and are susceptible to integration error accumulation, whereas CycleGAN-type architectures depend on approximate cycle-consistency objectives that provide only indirect and potentially decoupled constraints on reversibility. We introduce FlowCycle, an end-to-end framework that enables single-pass translation while ensuring exact reversibility in latent space. Specifically, we cast cross-domain transport as a discrete normalizing flow in a learned representation space, implemented via spatial affine coupling transformations. This design yields closed-form analytic inversion in one pass, obviates numerical solvers, and exposes an interpretable latent transition trajectory without requiring additional flow evaluations. Empirical results on synthetic digits (Multimodal MNIST), urban scenes (Cityscapes), and clinical multi-sequence brain MRI indicate state-of-the-art translation fidelity. Beyond quantitative performance, FlowCycle offers substantive practical advantages: in medical imaging, its traceable trajectories support transparent, clinician-auditable morphing for reliable synthesis of missing diagnostic sequences; in complex visual environments, its deterministic single-step inference facilitates real-time data simulation and robust cross-domain perception without computational bottlenecks. Our code are publicly available by https://anonymous.4open.science/r/FlowCycle-5634/