  A set A of positive integers is called a perfect difference set if every
nonzero integer has an unique representation as the difference of two elements
of A. We construct dense perfect difference sets from dense Sidon sets. As a
consequence of this new approach, we prove that there exists a perfect
difference set A such that A(x) >> x^{\sqrt{2}-1-o(1)}. We also prove that
there exists a perfect difference set A such that limsup_{x\to
\infty}A(x)/\sqrt x\geq 1/\sqrt 2.
