Thediffusionbehaviordrivenbyboundednoiseundertheinfluenceofacoupledharmonicpotentialisinvestigatedinatwo-dimensionalcoupled-dampedmodel.WiththehelpoftheLaplaceanalysisweobtainexactdescriptionsforaparticle’stwo-timedynamicswhichissubjectedtoacoupledharmonicpotentialandacoupleddamping.Thetimelagisusedtodescribethevelocityautocorrelationfunctionandmeansquaredisplacementofthediffusingparticle.Thediffusionbehaviorforthetimelagisalsodiscussedwithrespecttothecoupleditemsandtheamplitudeofboundednoise.