  We experimentally investigated the current noise in diffusive
Superconductor/Normal metal/Superconductor junctions with lengths between the
superconducting coherence length xi_Delta and the phase coherence length L_Phi
of the normal metal (xi_Delta < L < L_Phi). We measured the shot noise over a
large range of energy covering both the regimes of coherent and incoherent
multiple Andreev reflections. The transition between these two regimes occurs
at the Thouless energy where a pronounced minimum in the current noise density
is observed. Above the Thouless energy, in the regime of incoherent multiple
Andreev reflections, the noise is strongly enhanced compared to a normal
junction and grows linearly with the bias voltage. Semi-classical theory
describes the experimental results accurately, when taking into account the
voltage dependence of the resistance which reflects the proximity effect. Below
the Thouless energy, the shot noise diverges with decreasing voltage which may
indicate the coherent transfer of multiple charges.
