flow-match 2025

research

flow-match demo — Flow matching transports a Gaussian noise cloud into a two-moons distribution along the conditional flow path xₜ = (1−t)·x₀ + t·x₁.

Experiments with the flow matching framework for generative modeling. Flow matching learns a velocity field that transports samples from noise to data by integrating an ordinary differential equation (ODE) — a simpler, simulation- free alternative to training diffusion models.

What’s inside

A scikit-learn-like FlowMatcher API: fit, sample, and sample_trajectory (which returns the whole path from noise to data).
A neural velocity field (configurable MLP).
Multiple ODE solvers — Euler, Midpoint, and RK4 — to integrate the flow.
Several 2D toy datasets (moons, and friends) for quick experimentation.
Interactive marimo notebooks for visualization and intuition.

How it works

Pair each noise sample x0 with a data sample x1 and define the straight-line path x_t = (1 − t)·x0 + t·x1. The network is trained to predict the constant velocity x1 − x0 along that path; at sampling time you start from noise and integrate the learned velocity field with one of the ODE solvers. Higher-order solvers (Midpoint, RK4) reach the data distribution in fewer steps.

The animation above shows exactly this: a Gaussian cloud transported into a two-moons distribution along the flow.