Lots of interesting things I'd want to try here. Eg, the formulation of thinking of your probability distribution as a charge distribution opens up the possibility of adding negative charges. So you could have a regular positive data examples, but also some negative examples that the generative model tries extra hard to avoid.
I'd also be interested to see what happens when you "add the fields" for two different distributions over the same space. Seems like it would be interestingly different than regular superposition, and I'd really like to see what happens when you add together a dog image field to a cat image field.
I guess the current formulation where you only get the direction of the electric field and not the magnitude would cause problems there. Seems like an improvement might be to predict the actual potential instead of the field and then take the gradient. That would also guarantee that the field is curl-free, which it should be, but it doesn't seem to be enforced in the current paper. I think they don't try this because it's hard to get NNs to produce numbers across a wide range of orders of magnitude. Maybe separately predicting the normalized direction and something like the log of the magnitude would help here.