Deep conditional distribution learning via conditional Föllmer flow
This work addresses the challenge of conditional distribution learning for applications like density estimation and image generation, representing an incremental advancement with a novel method for a known bottleneck.
The paper tackles the problem of learning conditional distributions by introducing Conditional Föllmer Flow, an ODE-based deep generative method that approximates target conditional distributions from a Gaussian starting point, achieving superior performance over existing methods in experiments on nonparametric density estimation and image data.
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.