Y-shaped Generative Flows

2025-10-13

AI Summary

Contemporary continuous-time generative models typically exhibit a “V-shaped” transport: samples evolve independently from the prior to data points via straight-line trajectories, ignoring intrinsic shared structures among data. To address this, we propose Y-Flow—a Y-shaped generative flow that explicitly models hierarchical data relationships through a shared latent path: mass first moves collectively along a common trajectory, then bifurcates toward individual targets. Our key innovations include (i) a sublinear exponential velocity field that reduces transport cost and promotes efficient collective mass transport, breaking the V-shaped paradigm; and (ii) a scalable flow-matching objective built upon neural ordinary differential equations. Experiments on synthetic, image, and single-cell biological datasets demonstrate that Y-Flow significantly outperforms mainstream baselines—achieving superior distributional fidelity (e.g., lower FID and MMD) and improved sampling efficiency (reducing ODE integration steps by over 50%).

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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 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.

Problem

• Y-flows address V-shaped transport ignoring shared structure
• They introduce branching pathways with sublinear velocity cost
• The method improves distribution metrics and reduces integration steps

Innovation

• Y-shaped flows use shared pathways before branching
• Velocity-powered transport with sublinear exponent
• Neural ODE training objective for scalable implementation