Density estimation with normalizing flow in a minute

Normalizing flow is a generative deep neural network which can output a probability density function describing your data, by training a series of tunable transforms in the form of a neural network.
This can be useful for many purposes such as simulation-based inference. For example in one of my recent papers ( arxiv.org/abs/... ), we used a masked autoregressive flow network (arxiv.org/abs/...) to emulate a simple model and use the network as the likelihood function in an inference process.
In the future, this will help in connecting simulations which we do not know how to write down an analytical likelihood with real-world data, hence opening up an avenue to constraining real-world phenomenon with simulations directly.
Animation made with manim:
github.com/3b1...
Background music:
Awakening by Vlad Gluschenko | / vgl9
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Creative Commons Attribution 3.0 Unported License
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[@arvid8193]

I've tried to grasp this concept for a while now, and now I finally get it - thank you!

[@user-or7ji5hv8y]

This is a really good intuitive explanation.

[@katequark]

super cool 👍thanks for the explanation

[@hajvklkaj6462]

But how does it works for one variable? The flow must be monotonic function and thus will not give us many maxima and minima as seen here.

[@MathStuff1234]

Your first link with to your paper (2007.10350) is broken

[@physicskaze]

Thanks! this is fixed now

[@TragicGFuel]

so is this what's happening when generative models say they are predicting by sampling a probability distribution?
does that mean the machine learning model is essentially learning the mean and standard deviation of the data?

[@huanranchen]

great visualization!