Deep Conditional Generative Learning: Model and Error Analysis
Jinyuan Chang Zhao Ding Yuling Jiao Ruoxuan Li Jerry Zhijian Yang
We introduce an Ordinary Differential Equation (ODE) based deep generative
method for learning a conditional distribution, named the Conditional Follmer
Flow. Starting from a standard Gaussian distribution, the proposed flow could
efficiently transform it into the target conditional distribution at time 1.
For effective implementation, we discretize the flow with Euler's method where
we estimate the velocity field nonparametrically using a deep neural network.
Furthermore, we derive a non-asymptotic convergence rate in the Wasserstein
distance between the distribution of the learned samples and the target
distribution, providing the first comprehensive end-to-end error analysis for
conditional distribution learning via ODE flow. Our numerical experiments
showcase its effectiveness across a range of scenarios, from standard
nonparametric conditional density estimation problems to more intricate
challenges involving image data, illustrating its superiority over various
existing conditional density estimation methods.