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