Schrödinger bridge based deep conditional generative learning
This work addresses conditional generation problems for machine learning applications, representing an incremental improvement with a new method for a known bottleneck.
The paper tackles the problem of conditional generative modeling by introducing a novel Schrödinger bridge-based deep generative method that transforms a fixed point into a target conditional distribution using a discretized SDE with a neural network drift. The result shows that the generated samples exhibit higher quality compared to existing methods and can be used to estimate conditional density and related statistical quantities.
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 Schrödinger 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.