There’s a difference between intoxication and treating the chemical imbalance behind depression or anxiety. For one thing, treatments for anxiety only target the anxiety: they don’t impair the person the way that weed or alcohol does. (They can have other side effects, of course.)

Drugs for anxiety treatment do wear off, but not the same way that weed or alcohol does: something like Celexa takes a few weeks to build up in the system, and don’t lose effect 12-24 hours later if you miss a dose. I’m not sure how long you’d have to stop before it loses efficacy entirely.

I’m not Nancy Reagan, though: I would not advise people to self-medicate with booze or pot if they’re suffering from depression or anxiety, but I’m not going to preach at anybody who is doing so and thinks it’s working for them. I will say that I’ve seen that end badly, though. I can think of three people I’m close to who’ve tried it and have had problems with addiction: all of them are now sober and (I believe) on regular antidepressants.