Relations between RSA and Generalized Diffie-Hellman (GDH), factoring and GDH Definition: (The generalized Diffie-Hellman problem)
Let $n=pq$ for two large primes $p,q$. Given $x, x^a, x^b,n$, find $x^{ab}\pmod{n}$.

(1) Is there a known reduction from the GDH problem to the RSA problem (i.e. finding $m$ from $m^e\pmod{n}$)?
(2) Is there a known reduction from the GDH problem to integer factorization?
(That is, given an oracle which solves the second problem mentioned in (1)/(2), can you find an efficient algorithm which solves the GDH problem?)
Side-notes:

There is of course a reduction from GDH to DLOG, but I do not know of a reduction from DLOG to integer factorization or to the RSA problem.

It is known that the RSA problem limited to $e=2$ (i.e. finding square roots modulo $p$) can be reduced to integer factorization, but this is a non-interesting case. For a general $e$, AFAIK such reduction is not known.

Also, I am just as interested to hear about DH instead of GDH. (The DH problem is the same as GDH, but with a prime $p$ instead of semiprime $n$.)
Breaking the Generalized Diffie-Hellman (GDH) assumption is known to imply Factoring for Blum-integers. This is a result by Biham et al.
Since the (non)-equivalence of the RSA and Factoring assumptions is one of the biggest open questions in the RSA literature, it would be really surprising if there was a reduction from GDH to the RSA assumption, because then we would have the equivalence of the RSA and Factoring assumptions for Blum-integers given the result of Biham et al.