BenjaminDev/nflows

An Exploration into Normalizing Flows

What?

Normalizing Flows (NF) are a type of generative model. This means we can sample from the model. Let's say we want $I_{generated} \sim P_X(x)$ where $I$ is an image to be similar to:

from pathlib import Path
from random import choice as P_X
from PIL import Image

data_dir = Path("~/pictures")
images = [Image.open(o) for o in data_dir.glob("*.png")]
I_real = P_X(images)

One way of evaluating a genrative model $P_X(x)$ is to look a the images $I_{real}$ and $I_{generated}$. Do they look like they came from the same "place". Human qualitative assessment.

This is a useful goal in it's own right as seen by the Internet going bossy for StableDiffusion¹.

However, the goal in this work is to find a likelihood $P_{\theta}(X=x)$. This gives us the the probability of observing sample $X$ given $\theta$. $\theta$ is the "stuff" we looking for.

The idea!

Following a common way to make generative models we can: $$ P_{X}(x) = Z_{X}(z)|det $$

(Note: S) which can p $$ P_X(x) $$

Consider the model of a dice roll:

def dice():
    from

download ocean data:

wget -nd -r -l 1 -A png https://data-dataref.ifremer.fr/stereo/AA_2014/2014-03-27_09-10-00_12Hz/input/cam1

Footnotes

1. Diffusion models share similarities to NFs but they are stochastic. ↩