  Viale \cite{Viale_GuessingModel} introduced the notion of Generic Laver
Diamond at $\kappa$---which we denote
$\Diamond_{\text{Lav}}(\kappa)$---asserting the existence of a single function
from $\kappa \to H_\kappa$ that behaves much like a supercompact Laver
function, except with generic elementary embeddings rather than internal
embeddings. Viale proved that the Proper Forcing Axiom (PFA) implies
$\Diamond_{\text{Lav}}(\omega_2)$. We strengthen his theorem by weakening the
hypothesis to a statement strictly weaker than PFA. We also show that the
principle $\Diamond_{\text{Lav}}(\kappa)$ provides a uniform, simple
construction of 2-cardinal diamonds, and prove that
$\Diamond_{\text{Lav}}(\kappa)$ is quite prevalent in models of set theory; in
particular:
  1) $L$ satisfies $\Diamond_{\text{Lav}}^+(\kappa)$ whenever $\kappa$ is a
successor cardinal, or when the appropriate version of Chang's Conjecture
fails.
  2) For any successor cardinal $\kappa$, there is a $\kappa$-directed closed
class forcing---namely, the forcing from Friedman-Holy \cite{MR2860182}---that
forces $\Diamond_{\text{Lav}}(\kappa)$.
