Schr\"odinger bridge based deep conditional generative learning

TL;DR

This paper introduces a Schr"odinger bridge-based deep generative model that learns conditional distributions through a stochastic differential equation, producing high-quality samples for both low- and high-dimensional data.

Contribution

The work presents a novel Schr"odinger bridge approach for deep conditional generative learning using SDEs and neural networks, enhancing sample quality without explicit density estimation.

Findings

Generated samples have higher quality than existing methods.

Samples can be used to estimate conditional densities and statistics.

Applicable to both low- and high-dimensional data.

Abstract

Conditional generative models represent a significant advancement in the field of machine learning, allowing for the controlled synthesis of data by incorporating additional information into the generation process. In this work we introduce a novel Schr\"odinger bridge based deep generative method for learning conditional distributions. We start from a unit-time diffusion process governed by a stochastic differential equation (SDE) that transforms a fixed point at time $0$ into a desired target conditional distribution at time $1$. For effective implementation, we discretize the SDE with Euler-Maruyama method where we estimate the drift term nonparametrically using a deep neural network. We apply our method to both low-dimensional and high-dimensional conditional generation problems. The numerical studies demonstrate that though our method does not directly provide the conditional density estimation, the samples generated by this method exhibit higher quality compared to those obtained by several existing methods. Moreover, the generated samples can be effectively utilized to estimate the conditional density and related statistical quantities, such as conditional mean and conditional standard deviation.