Reconsider the softmax distribution

[cheind]

PixelCNN++ argues that neighboring intensity usually correlate is not captured by the softmax distribution. Instead, they propose a mixture model consisting of the logitic distribution (like normal but with heavier tails).
https://arxiv.org/pdf/1701.05517.pdf

[cheind]

also add bits-per-dim metric that measures how many bits are required to encode pixel intensities.
see E.2 of https://arxiv.org/pdf/1705.07057.pdf
https://uvadlc-notebooks.readthedocs.io/en/latest/tutorial_notebooks/tutorial11/NF_image_modeling.html

[cheind]

See also for how to optimize based on cdf
https://github.com/Rayhane-mamah/Tacotron-2/issues/155