Noisy images produced by adding same variance differs in MSE and Psnr values calculated w.r.t same ref image why?

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When I add Gaussian noise with 0 mean & variance =0.3 to the same reference image several times and save these set of images in a folder and then check the MSE and PSNR w.r.t Reference image the output MSE PSNR values are differing.Why is it so? How is the noise been added... is it because of random nature..?
Please can anyone help me out in understanding this issue..?

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