Flow Matching: A Visual Introduction

6 months ago

Flow Matching (FM) is a technique for training generative models by learning to transport samples from a simple distribution (e.g., Gaussian noise) to a complex target distribution (e.g., images, videos).
The post demonstrates a toy example where a 1D Gaussian noise distribution is mapped to a bimodal target distribution using linear flow matching.
The flow matching model predicts a velocity field that describes how to move samples from the noise distribution to the target distribution over time steps t ∈ [0, 1].
Training involves minimizing the expected reconstruction error of the velocity field using straight-line reference paths between noise and target samples.
The model is implemented as a simple neural network trained with gradient-based optimization (Adam optimizer) to predict the velocity field.
At inference, samples are generated by integrating the learned velocity field using Euler integration from noise samples to target samples.
Visualizations include the learned velocity field, path densities, and comparisons between the target distribution and reconstructed samples.
Flow matching can be extended to more complex distributions and higher dimensions, though it requires more sophisticated models and sampling strategies.

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