Does the One Time Pad rely on confusion or diffusion?
The One-Time Pad employs neither confusion nor diffusion, as defined by Shannon:


  "Two methods (other than recourse to ideal systems) suggest themselves for frustrating a statistical analysis. These we may call the methods of diffusion and confusion. In the method of diffusion the statistical structure of $M$ which leads to its redundancy is “dissipated” into long range statistics—i.e., into statistical structure involving long combinations of letters in the cryptogram. [...] The method of confusion is to make the relation between the simple statistics of $E$ and the simple description of $K$ a very complex and involved one."


(It's worth noting that, to really understand these definitions, you should read the full paper in detail.  In particular, the earlier definition of a "strongly ideal cipher" that the text alludes to is kind of nontrivial, and not something commonly encountered in modern cryptography.)

In the one-time pad, each ciphertext symbol depends on exactly one message symbol and one key symbol.  Thus, there is no diffusion, in the sense used by Shannon, since the relationship between the message $M$ and the ciphertext $E$ is trivial, nor can there be any confusion, since the relationship between the key $K$ and the ciphertext $E$ is equally trivial.

Instead, the perfect secrecy of the one-time pad follows from the fact that the use of a random one-time key masks any redundancy in the plaintext: without knowledge of the key, the ciphertext is statistically independent of the plaintext, and thus no ciphertext statistics can reveal any information about the message.  (Such statistics can reveal information about the key, if the attacker can guess some of the plaintext; but since the key is never reused, this makes no difference.)

It should be noted that this does not contradict Shannon's statements in any way: the section where the terms "confusion" and "diffusion" are defined is explicitly concerned only with non-ideal (in the sense defined earlier) ciphers using keys of bounded length.  The one-time pad is not such a cipher, and so the statistical analysis techniques that confusion and diffusion are supposed to prevent do not (necessarily) apply to it.  Furthermore, Shannon never claims that confusion and diffusion would be the only ways to protect a cipher from statistical analysis; merely that they are two obvious and general ways to (attempt to) do so.