I wrote an interactive article explaining the geometric intuition behind Rectified Flows. I visually explain why flow-models tend to learn curved trajectories, why this is bad for sampling latency, and a relatively simple technique for mitigating it. Check it out! Link 👇

Most of the visualizations have interactive elements that work by running an actual flow model on the front end using Tensorflow.js. It should even work on most mobile devices. Link to blog:

This project is a part of a broader effort to explain and visualize flow-based generative models with interactive visualization. Check out the code here:

Very nice, but IIRC in very high dimensions the paths straighten out quite a lot even with vanilla flow matching, so these 2D examplrs can be a bit misleading for realistic generative models... I even remember some papers that gave some theoretical explanation for this.

love this! curved flows always felt like data taking the scenic route. straightening them shaved 30% off my sampling time. visuals were super clear, thanks!

those curved trajectories always wreck sampling latency

sweet 😋

crazy

Super cool thanks for sharing!

I am basically reading this the same way the chimps investigate the obelisk at the start of 2001: A Space Odyssey but it's a beautiful document.

Beautiful, bro

🔥❤️

What clicked for me is that this isn’t just about faster sampling... it’s about constraint geometry!! Curvature is a symptom of mismatch between learned flow and data manifold. Rectification feels like enforcing the right geometry, not optimizing around the wrong one.

Pretty awesome work, Alec! Loved how you explained a complex topic in such a simple way. Really good!

Cool Stuff, lot of people are so busy trying to keep up with new models and techniques coming out everyday sometimes we forget to actually absorb the material, the true underlying principles underneath.

Very cool post, the visualizations are great.

Thank you!

Nice! That sounds super insightful and useful for anyone diving into flow models.#waterlystfeb2

@alec_helbling, your explanation of rectified flows will help many understand this complex topic better.

curious how this compares to normalizing flows in other domains

interesting / arXiv also?