Both can be translated by "at least" but "du moins" is a qualifying statement while "au moins" talks about the minimum. Here is an example:
Il est allé se coucher, du moins je le crois. -- He went to sleep, at least that's what I believe.Il a dormi au moins 8 heures. -- He slept at least 8 hours.
-- Chris (not a native speaker).
A typo struck again in my previous post. It should be "il a dormi 8 heures...".
... and of course also "il est allé se coucher..."
I do wish there were some way to go back and correct them.
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