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What is the main architectural difference between DCGAN and WGAN? For which problems each models can be more useful than the other one?

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DCGAN is more about network architecture alterations, while WGAN is an change to the loss function. There's nothing stopping you from using the DCGAN architecture with the WGAN objective function: all this means is minimizing an approximate Wasserstein loss, rather than a Jensen-Shannon divergence, using a particular network architecture. The WGAN (or its followups, e.g. WGAN-GP) objective is agnostic to the architecture. The only thing (that I can think of) that you need to watch for is the use of batch norm: DCGAN recommends putting it everywhere, but (at least for WGAN-GP) it messes with statistics of the critic regularization.

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