Fast Neural Style Transfer works like this: Each style image is actually trained on a neural network outside of the browser (using Python on Tensorflow) for around 6+ hours with a GPU.

The output is a neural network that can take any content image and outputs it in the style it was trained on.

The browser does this: 1. Downloads the model (6.6MB~) for the particular style. 2. Does one pass through the content image and outputs the styled image.

No training is done in the browser whatsoever.