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What would be a good similarity metric for comparing two such distributions (2D or 3D), if they each represent different perturbations from different backgrounds?

In a simple case where the distribution is known, I was looking into Kullback-Leibler divergence, earth mover's distance, or Bhattacharyya distance, but I would first need to first consider how to properly extend them to handle this problem (if it makes sense).

Alternatively, I could just integrate their difference.

What do you all think?