The answer to this can be found in Chapter 9 of Collapse.  Since I only have this book on Kindle, I cannot give you a page number, but Amazon’s searchable copy indicates that the relevant discussion begins on p. 304 of that edition.

The first relative advantage that Japan enjoys has to do with its environment.  This environment allows trees to grow back more quickly in Japan than they would in some other parts of the world.  Specifically, Japan has high rainfall and fertile soil because of volcanic fallout and because dust blows in from mainland Asia.  In addition, Diamond says that Japan has “young soils.”  These factors allow relatively rapid reforestation to occur.

The second set of relative advantages was social.  Japan did not have sheep and goats.  This meant that its land was not overgrazed.  The problem of overgrazing was also averted because the onset of peace with the Tokugawa unification of Japan reduced the need for cavalry horses.  Japan also had abundant seafood resources, meaning that forests were not as important as a source of fertilizer and protein.

The final advantages were political.  The Tokugawa shoguns were secure and confident in the idea that they would be in control for generations.  Because of this, they were willing to implement policies that were good in the long term even if they were not great in the short term.  Japan also was unified and isolated.  This meant that Japanese knew that they could not get out of their problems through conquering others (at least not in Tokugawa times).

All of these were relative advantages enjoyed by Japan that allowed it to recover from its deforestation.