The noise is water pulsing through the water lines, resonating through the floor or vibrating up against... something.
You will need to isolate the noise. The pump could be coming loose from its mount, a water line may come up against a bulkhead, or the floor, or something similar. Try just hot water, and then just cold water to see which causes the noise. Could be both, of course. But if just one or the other it wouldn't be from the pump - you'll just need to find the offending water line. If it comes from the pump, look at the rubber feetl; one may have split or broken. Or the pump could be about to fail internally.
Once you find the source, you need to cushion it. Some of that insulating foam for water pipes works great for the water lines.
An accumulator tank can also help.