In spectre itself, leaving noiseseed unspecified results in a different seed for each invocation of the simulator. Unfortunately ADE forces you to set noiseseed to a number greater than 0.
You can workaround this by not checking the "Transient Noise" checkbox, but instead using the Additional Parameters field on the Misc tab of the transient Options form. If you enter "noisefmax=1G noisefmin=1K" or whatever you want in this field, then you'll get a different seed on each run.
Bear in mind that if ADE is in "interactive" mode, then the seed won't change until spectre actually exits (you have to hit the "Stop" button). If using APS, it's always in "batch" mode, or you can use:
envSetVal("spectre.envOpts" "controlMode" 'string "batch")
before starting ADE to force batch mode. Note that you lose a little performance if using parametric analysis or variable-only changes in ADE because it has to restart the simulator each time, if you use this setting.
I think it would be reasonable to have ADE allow a blank value for the seed - there was some discussion in CCR 780017 about this, but it didn't lead to an enhancement. So if you want this, please contact customer support and request this so that a CCR can be filed on your behalf (best if it comes from a customer rather than just me!).