Generative Modeling by Value-Driven Transport

2026-05-21

AI Summary

This work addresses the challenges of curved transport trajectories, low simulation efficiency, and limited scalability in generative modeling by introducing a value-driven transport framework. Grounded in discrete-time stochastic control theory, the approach formulates measure transport as a linear program and explicitly constructs the optimal value function via dual variables, yielding a deterministic transport policy that obviates the need for simulation. The method naturally accommodates conditional generation and unpaired data translation, producing straighter transport paths and faster simulation. Empirical evaluations demonstrate its superiority over existing flow-based models, diffusion models, and Schrödinger bridge approaches across multiple tasks, achieving both high efficiency and strong scalability.

Abstract

We propose a new framework for generative modeling based on a discrete-time stochastic control formulation of measure transport. Adapting classic results from control theory, we formulate our problem as a linear program whose dual variables correspond to the \emph{optimal value function} of the control problem, which directly encodes the optimal control policy. Exploiting this LP formulation, we develop an efficient simulation-free primal-dual algorithm for computing approximately optimal value functions and the associated \emph{value-driven transport} (VDT) policies which approximate the true optimal policy. We show that well-trained VDT policies enjoy numerous favorable properties in comparison with other state-of-the-art methods based on flows, diffusions, or Schrödinger bridges: they lead to straight transport paths which can be simulated quickly and robustly, and can be enhanced in all the same ways as diffusion and flow-based models (e.g., conditional generation, classifier-free guidance, unpaired data-to-data translation are all easy to incorporate). We evaluate our methodology in a range of experiments, with results that indicate strong performance and good potential for scalability.

Problem

• generative modeling
• measure transport
• stochastic control
• optimal policy
• value function

Innovation

• value-driven transport
• measure transport
• stochastic control
• primal-dual algorithm
• generative modeling