Beyond Random Couplings: Spherical Noise Alignment in Generative Flows

Flow matching models are typically trained using independent noise-data couplings, forcing the network to resolve conflicting conditional fields by learning highly curved velocity trajectories. This leads to slow iterative sampling, as numerical ODE solvers require many Neural Function Evaluations (NFEs) to track these paths accurately. While Minibatch Optimal Transport (OT) straightens the vector field by pairing noise and data samples to minimize transport cost, its reliance on discrete matching within small batches leaves it fundamentally bottlenecked by high-dimensional estimation variance. To overcome this limitation, we introduce continuous coupling via noise optimization, a framework that extends beyond discrete index matching towards continuously shaping noise endpoints. As a concrete realization, we present Spherical Noise Alignment (SNA), an online algorithm that rotates source samples through balanced attractive and repulsive forces. The framework aligns noise samples with target data points during training while preserving prior fidelity. This allows seamless sampling from standard Gaussian noise at inference. Experimental results show that our approach improves source-target alignment, significantly reduces path curvature, and achieves superior sample fidelity in few-step (1–4 NFE) sampling regimes.