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SN74LVT125-Q1: Many Output Channels - Output Ripple

Part Number: SN74LVT125-Q1

I am using the mentioned part in the following schematic:

As per the advice of a previous question, I included filtering on a smaller version of this schematic (with only 7 outputs). However, I am still finding quiet a bit of ripple on the output with my oscilloscope, using a 4V pulse generator at 1MHz.

I have tried additional capacitors to filter the power to the individual ICs further, but this doesn't seem to be having an effect. What might be the problem?

Edit: Here is an additional picture showing the power waveform in purple.