# Deep conditional distribution learning via conditional F"ollmer flow

arXiv: https://arxiv.org/abs/2402.01460 · HTML: https://mlsanity.com/paper/2402.01460/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Feb 2024.

## Built on by (most cited first, 9 of 9)

- [Convergence of Continuous Normalizing Flows for Learning Probability Distributions](https://mlsanity.com/paper/2404.00551/) (2024)
- [Broadening Target Distributions for Accelerated Diffusion Models via a Novel Analysis Approach](https://mlsanity.com/paper/2402.13901/) (2024)
- [Convergence Analysis of Flow Matching in Latent Space with Transformers](https://mlsanity.com/paper/2404.02538/) (2024)
- [Latent Schr"odinger Bridge Diffusion Model for Generative Learning](https://mlsanity.com/paper/2404.13309/) (2024)
- [Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers](https://mlsanity.com/paper/2410.13746/) (2024)
- [Inference-Time Alignment for Diffusion Models via Variationally Stable Doob's Matching](https://mlsanity.com/paper/2601.06514/) (2026)
- [Schr"odinger bridge based deep conditional generative learning](https://mlsanity.com/paper/2409.17294/) (2024)
- [Deep Generative Demand Learning for Newsvendor and Pricing](https://mlsanity.com/paper/2411.08631/) (2024)
- [Optimal Mixture-of-Experts Model Averaging for Conditional Generative Models](https://mlsanity.com/paper/2607.04360/) (2026)

## Abstract (arXiv)

We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional F"ollmer 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.