Deep conditional distribution learning via conditional Föllmer flow
CoRR(2024)
Abstract
We introduce an ordinary differential equation (ODE) based deep generative
method for learning conditional distributions, named Conditional Föllmer
Flow. Starting from a standard Gaussian distribution, the proposed flow could
approximate the target conditional distribution very well when the time is
close to 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 also establish the convergence result for the
Wasserstein-2 distance between the distribution of the learned samples and the
target conditional 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.
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