I already quit smoking about 3 months ago. I was smoking 1-3 times a day and completely stopped altogether on May 1st (yes I remember the exact date, lol). It took a while for the stuff to clear out of my system, but my dream recall and frequency of lucidity has gradually increased ever since then. Anyway, heres the form:

Before:
Age: 19
Sex: Male
Your usual Dream Recall: DR2 (usually recalled a couple scattered fragments or nothing at all... usually nothing)
Your Dream's usual Level of Vividness: DV3
Usual frequency of Lucid Dreams: L3 (about once every other month)

3 months later...

After:
Method used: 1
Your Dream Recall after the Experiment: DR8 (1-3 per night)
Your Dream's Level of Vividness after the Experiment: DV7
Frequency of Lucid Dreams after the Experiment: L7 (once or twice a week)
If you think that any of the numbers that I chose should be adjusted (based on the comments I left by them), let me know.

All this improvement was very gradual! For the first few weeks after quitting, I saw no improvement whatsoever, and then over the course of the next 2 months it got better and better.
Note: My results might be somewhat skewed, because in addition to quitting marijuana, I also took up daily meditation around the tail end of May. So these improvements are likely a combination of these two factors.

Anyway, here's something I read online a while ago that is very relevant: Detoxing from Marijuana. Here's the most relevant part:
Originally posted by Marijuana Anonymous
What are some of the more common symptoms?

By far the most common symptom of withdrawal is insomnia. This can last from a few nights of practically no sleep at all, up to a few months of occasional sleeplessness. The next most common symptom is depression (that is, if you're not euphoric), and next are nightmares and vivid dreams. Marijuana use tends to dampen the dreaming mechanism, so that when you do get clean the dreams come back with a crash. They can be vivid color, highly emotional dreams or nightmares, even waking up then coming back to the same dream. The very vivid, every-night dreams usually don't start for about a week or so. They last for about a month at most and then taper off. "Using" dreams (dreams involving the use of marijuana) are very common, and although they're not as vivid or emotional as at first, they last for years and are just considered a normal part of recovery.
Personally, I didn't experience a "crash" of dreams like they describe, which would suggest an REM-rebound effect similar to that of alcohol. Mine was gradual and progressive, and was probably a just a result of being more clear-headed.