Y-shaped Generative Flows

Modern continuous-time generative models often induce V-shaped transport: each sample travels independently along nearly straight trajectories from prior to data, overlooking shared structure. We introduce Y-shaped generative flows, which move probability mass together along shared pathways before branching to target-specific endpoints. Our formulation is based on novel velocity-powered transport cost with a sublinear exponent (between zero and one). this concave dependence rewards joint and fast mass movement. Practically, we instantiate the idea in a scalable neural ODE training objective. On synthetic, image, and biology datasets, Y-flows recover hierarchy-aware structure, improve distributional metrics over strong flow-based baselines, and reach targets with fewer integration steps.