# Earth Mover's Distance vs. Frechet Distance

Both Earth Mover’s Distance vs. Frechet Distance meaure the distances of two distributions.

Can we use Earth Mover’s Distance to evaluate GAN ?
Can we use Frechet Distance to implemment a FGAN similar to WGAN ?

Hi mc04xkf!
Hope you are doing well. Yes, both Earth Mover’s distance and Frechet’s distance measure the similarity of two distributions. But the intuition and motivation behind them are different.

Earth Mover’s distance measures how different these two distributions are, by estimating the amount of effort it takes to make the generated distribution equal to the real. The Fréchet distance, on the other hand, is a measure of the similarity between two curves or paths in a metric space.
Basically, W-loss approximates Earth Mover’s distance, minimal w-loss → minimum Earth Mover’s distance - > more similar distributions (we are making the generator to generate something very similar to the original distribution). So, if you want to use Frechet distance, then you have to find a loss function which approximates Frechet distance so that you can minimize that.
Will that make sense? will that address mode collapse? or will it perform worse than BCE loss? - one has to think about it. Maybe you can find such a loss function and share your results here !
Have a great day!
Regards,
Nithin

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A thing to note is, using FID directly is impractical since it takes so long to compute.