# Do I have to downsample the input and upsample the output of the neural network when implementing the NICE algorithm?

Consider that my input is an RGB image. The size of my image is $$N\times N$$. I'm trying to implement NICE algorithm presented by Dinh. The bijective function $$f: \mathbb{R}^d \to \mathbb{R}^d$$ maps $$X$$ to $$Z$$. So I have $$p_Z(Z)=p_X(X)$$.

What I can't understand is that $$N$$ is much bigger than $$d$$. Does this mean that I should downsample the inputs? Does the resulting loss function change if I add a downsampling layer at the beginning of the neural net and also add an upsampling layer at the end of the net?