Is there any metric for calculating how natural a single image is given a dataset of the same class images?

Suppose there is a dataset $$D$$ of images. We have enough number $$n$$ of images in the dataset and all the images are of a single class.

Suppose I generated a new image $$I$$, which is not present in the given dataset, of the same class using a generator neural network. I want to calculate how natural the image $$I$$ is wrt the dataset $$D$$

$$m(I, D) =$$ how natural the image $$I$$ with respect to dataset $$D$$ of images.

I don't want metrics that are applied to a bunch of generated images. I have only one generated image.

I came up with a naive metric

$$m(I, D) = \sum\limits_{x \in D} (x-I)^2$$

where $$x-I$$, difference between two images, is defined as the sum of pixel differences of both the images i.e., $$x-I = \sum\limits_{x_i \in x, I_i \in I} \|x_i - I_i\|$$

But, this measure shows how similar the new image $$I$$ w.r.t is to the set of images in my dataset at the pixel level. I want a measure of how natural it is.