Flow Matching

Flow Matching is a generative modeling technique that builds upon the ideas of continuous normalizing flows and probability flow ODEs, offering an alternative training approach for generative models.

Overview

Flow Matching defines a continuous-time transformation from a simple distribution (like a Gaussian) to a complex target distribution. Unlike traditional normalizing flows, flow matching doesn't require computing the Jacobian determinant, making it more flexible and computationally efficient.

Key Concepts

  • Vector Fields: Learning a vector field to represent the continuous-time flow
  • Straight-line Paths: Using simple paths between distributions
  • Conditional Flow Matching: Extending to conditional generation
  • ODE-based Generation: Sampling by solving an ordinary differential equation

Relation to Other Models

  • Diffusion Models: Flow matching can be seen as a generalization of score-based diffusion models
  • Normalizing Flows: Similar concept but with different training objectives
  • Optimal Transport: Connection to optimal transport theory

Advantages

  • Flexible Architecture: No invertibility requirement
  • Efficient Training: More efficient than score matching in some cases
  • Theoretical Guarantees: Well-founded mathematical framework
  • Stable Training: Often more stable than adversarial approaches

Applications

  • Image Generation: Creating realistic images
  • Shape Generation: 3D shape synthesis
  • Audio Synthesis: Generating audio waveforms
  • Density Estimation: Learning complex distributions

Awesome Flow Matching

References