# Flow Matching for Generative Modeling

**Authors:** Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, Matt Le  
**arXiv:** [2210.02747](https://arxiv.org/abs/2210.02747)  
**Date:** 2022-10-06  
**Summary page:** https://www.summarizepaper.com/en/paper/2210.02747v1/

## Key points

- Authors introduce Flow Matching (FM) for generative modeling using Continuous Normalizing Flows (CNFs)
- FM enables training of CNFs at an unprecedented scale by regressing vector fields of fixed conditional probability paths
- FM works with a broad range of Gaussian probability paths, including diffusion paths
- Using FM with diffusion paths offers a more robust and stable alternative for training diffusion models
- Flow Matching allows training CNFs with non-diffusion probability paths like Optimal Transport (OT) displacement interpolation
- Alternative paths are more efficient than diffusion paths, leading to faster training and sampling processes and improving generalization capabilities
- Applying Flow Matching to ImageNet data achieves state-of-the-art performance in likelihood estimation and sample quality
- Compatibility with off-the-shelf numerical ODE solvers enables fast and reliable sample generation

## Summary

In their paper titled "Flow Matching for Generative Modeling," authors Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le introduce a groundbreaking paradigm for generative modeling using Continuous Normalizing Flows (CNFs). This novel approach enables the training of CNFs at an unprecedented scale by introducing Flow Matching (FM), a simulation-free method that involves regressing vector fields of fixed conditional probability paths. FM is designed to work with a broad range of Gaussian probability paths, including diffusion paths as specific instances. The authors demonstrate that employing FM with diffusion paths offers a more robust and stable alternative for training diffusion models. Moreover, Flow Matching paves the way for training CNFs with non-diffusion probability paths, such as Optimal Transport (OT) displacement interpolation. These alternative paths are shown to be more efficient than diffusion paths, leading to faster training and sampling processes while also improving generalization capabilities. By applying Flow Matching to ImageNet data, the authors achieve state-of-the-art performance in terms of both likelihood estimation and sample quality. One key advantage of using Flow Matching is its compatibility with off-the-shelf numerical ODE solvers, enabling fast and reliable sample generation. Overall, this innovative approach opens up new possibilities for generative modeling by enhancing scalability, stability, efficiency, and performance across various applications in machine learning and artificial intelligence.