Ask what should change when the equation is manipulated, then let the visualization test that expectation.
Foundation Lab
Flow Matching & Rectified Flows
Simpler than diffusion: no noise schedule to tune
#83Flow MatchGenerative Models
key equation
\frac{dx_t}{dt} = v_\theta(x_t, t)Selected Foundation Object
Keep the equation fixed; move through the evidence.
Concept 83 of 100Flow MatchGenerative Models / Phase 4: Generative modeling families
Current question
Diffusion = learn to denoise; flow = learn velocity directly
\frac{dx_t}{dt} = v_\theta(x_t, t)Use the runnable panel, the key equation, and canonical papers as separate forms of evidence for the same object.
The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.
This atlas page keeps the working demo; the domain notebook carries the fuller Intuition -> Math -> Code -> Demo sequence.
Why It Matters for Modern Models
- Simpler than diffusion: no noise schedule to tune
- Rectified flows enable 1-4 step generation
- State-of-the-art: Stable Diffusion 3 uses flow matching
What Tutorials Skip
What is still poorly explained in textbooks and papers:
- Diffusion = learn to denoise; flow = learn velocity directly
- Straight paths are easiest to approximate with few steps
- Simulation-free: no sampling during training
Interactive Visualization
Core Math (Optional Deep Dive)
If you want intuition first, start with the key equation and the visualization. Come back here for the full walkthrough.
Key Equation
Learn vector field transporting noise to data:
Conditional flow matching:
Rectified flow: Straight paths