We present results of searches for diphoton resonances produced both inclusively and also in association with a vector boson (W or Z) using 100 pb-1 of pp̄ collisions using the CDF detector. We set upper limits on the product of cross section times branching ratio for both pp̄→γγ+X and pp̄→γγ+ W/Z. Comparing the inclusive production to the expectations from heavy sgoldstinos we derive limits on the supersymmetry-breaking scale √F in the TeV range, depending on the sgoldstino mass and the choi...