In hole-doped high Tc cuprate superconductors, the Nernst effect suggests that the superconducting transition comes from the loss of long-range phase coherence, instead of the vanishing of the pair condensate. We present the observation of diamagnetism of the pair condensate above Tc on various families of cuprates LSCO, Bi2201, Bi2212, and YBCO. The diamagnetic magnetization is measured using torque magnetometry under magnetic field up to 45 T. we show that the diamagnetic magnetization appears at Tonset high above Tc. Constructing the phase diagram of both LSCO and Bi 2201, we find that Tonset agrees with the onset temperature of the vortex Nernst signals. Further magnetization measurements in heavily underdoped LSCO samples demonstrate the existence of the the temperature vortex liquid state driven by quantum phase fluctuation, even though the samples have turned insulating. These results, together with our recent measurements on the stripe-ordered 1/8-LBCO samples, provide thermodynamic evidence of surviving pair condensate in the pseudogap state in high Tc cuprates.