Does this diagram represent several LSTMs, or one through several timesteps? I'm trying to read this paper describing Google's LSTM architecture for machine translation. It features this diagram on page 4:

I'm interested in the encoder block, on the left. Apparently, the pink and green cells are LSTMs. However, I can't tell if the x-axis is space or time. That is, are the LSTM cells on a given row all the same cell, with time flowing forward from left to right? The diagram on the next page in the paper seems to suggest that.
are the LSTM cells on a given row all the same cell, with time flowing forward from left to right?

Yes this is correct
The x-axis on this figure is basically the time axis. Essentially all pink boxes in the same row are the same LSTM cell, with different inputs from the same sequence. At each timestep, the cell takes an input and produces an output which is fed to the next layer. At the 8-th layer, the outputs over all timesteps are inputted at the same time to the attention layer.