Upsample a array sampled from Normal distribution without change its distribution

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If I upsample a 2D array which is sampled from Normal distribution(that's say torch.rand(16,16) for example), what I want is a new array which is also followed Normal distribution.

A common way to upsample is use linear interpolation(bilinear, trilinear ...), but the variance in new array is changed. For example, the mean of two Normal distribution has a variance of 1/4.

So, is there any method can upsample a 2D array without change its distribution?