Stream-level Flow Matching with Gaussian Processes

Area of Science:

• Machine Learning
• Generative Models
• Deep Learning

Background:

• Continuous normalizing flows (CNFs) are powerful generative models.
• Flow matching (FM) and conditional flow matching (CFM) are training algorithms for CNFs.
• CFM learns vector fields via regression, but can suffer from variance.

Purpose of the Study:

• To extend the conditional flow matching (CFM) algorithm.
• To reduce variance in vector field estimation for improved sample quality.
• To leverage Gaussian processes (GPs) for enhanced CFM training.

Main Methods:

• Introduced conditional probability paths along latent stochastic paths ('streams').
• Modeled these streams using Gaussian process (GP) distributions.
• Applied the generalized CFM to image and neural time series data.

Main Results:

• Demonstrated reduced variance in the estimated marginal vector field.
• Achieved improved sample quality under common generative metrics.
• Showcased the ability to link correlated data points, like time series.

Conclusions:

• The proposed GP-enhanced CFM method offers a simulation-free approach to training CNFs.
• This generalization effectively reduces training variance at moderate computational cost.
• The method shows promise for various generative modeling applications, including time series data.