A search is presented for photonic signatures motivated by generalized models of gauge-mediated supersymmetry breaking. This search makes use of 20.3  fb−1 of proton-proton collision data at s√=8  TeV recorded by the ATLAS detector at the LHC, and explores models dominated by both strong and electroweak production of supersymmetric partner states. Four experimental signatures incorporating an isolated photon and significant missing transverse momentum are explored. These signatures include events with an additional photon, lepton, b-quark jet, or jet activity not associated with any specific underlying quark flavor. No significant excess of events is observed above the Standard Model prediction and model-dependent 95% confidence-level exclusion limits are set.