It's from same GAN though, C(x_r) and C(x_f) come from the same neural network. It's how realistic real data is compared to fake data (and vice-versa) as determined by C (discriminator without activation function).
"Relative probability" is only correct for standard GAN, not for other GANs which don't estimate a probability.
My first name was "Critic's difference" since it's literally C(x_r)-C(x_f) so its the difference in critics, but it felt really unclear, it doesn't give the reader any sense of what it is about. Relativism/Relativistic is better since it's to say that it really doesn't matter if the data looks real, what matters if how realistic is real data relative to fake data (and vice versa). The frame of reference is important here.
It's not even probability in standard GAN is it? Since you are taking the difference before the sigmoid. It can't really be interpreted as probability until it the range is clamped. Critic's difference or Critical Difference would be a better term perhaps.
Since sigmoid(C(x_r)) = p(x_r is real) and C(x_f) = p(x_f is real), the sigmoid of the difference expresses some probability that that x_r looks more real than x_f or vice versa (depending on whether it is C(x_r) - C(x_f) or C(x_f) - C(x_r)). Not sure whether there is a probabilistic interpretation of the difference, but it looks so simple that there maybe is one. I couldn't find one in the paper.
