Y-shaped Generative Flows

Arip Asadulaev, Semyon Semenov, Abduragim Shtanchaev, Eric Moulines, Fakhri Karray, Martin Takáč

Keywords: Generative Flows, Normalizing Flows, Optimal Transport

TL;DR: Generative models with branched flow structures

Abstract: 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 a novel velocity-driven objective with a sublinear exponent (between zero and one), this concave dependence rewards joint, 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.

Primary Area: generative models

Submission Number: 2616