You can't. The histogram alone does not have that information in it. As you can imagine, it's possible for two totally different images to have the same histogram and not have any pixels that are the same. Just imagine turning your image upside down. Now it's possible for every pixel in the upside down image to have a different value than the original, and so every pixel could be considered as noise, yet they have the identical histogram.
If we can add additional information, which is to assume that your images are aligned, then the noisy version might have a somewhat wider histogram. But a better way would be to subtract the images first, then take a histogram of the difference. If there is no difference it should be a big spike at zero. If there's spread then there are some differences.
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