Generative Modeling by Value-Driven Transport

TL;DR

This paper introduces a novel measure transport framework for generative modeling using a stochastic control approach, resulting in efficient, robust, and versatile generative policies.

Contribution

It develops a primal-dual algorithm for value-driven transport policies based on LP formulation, offering advantages over flow-based methods.

Findings

VDT policies produce straight, quickly simulatable transport paths.

The method shows strong performance across various experiments.

VDT can incorporate features like conditional generation and guidance.

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 Schr\"odinger 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.