The title of this post is clearly misleading, even with the word 'might' in it. Neurogenesis in mice was detected when the mice were given Prozac or HU210, a cannabinoid different from the active ingredient in marijuana.

The article then goes on to describe another experiment in which mice dosed with D9-tetrahydrocannabinol (the cannabinoid in weed) did not show any signs of neurogenesis, no matter what dose was used.