  We present Polarity Sampling, a theoretically justified plug-and-play method
for controlling the generation quality and diversity of pre-trained deep
generative networks DGNs). Leveraging the fact that DGNs are, or can be
approximated by, continuous piecewise affine splines, we derive the analytical
DGN output space distribution as a function of the product of the DGN's
Jacobian singular values raised to a power $\rho$. We dub $\rho$ the
$\textbf{polarity}$ parameter and prove that $\rho$ focuses the DGN sampling on
the modes ($\rho < 0$) or anti-modes ($\rho > 0$) of the DGN output-space
distribution. We demonstrate that nonzero polarity values achieve a better
precision-recall (quality-diversity) Pareto frontier than standard methods,
such as truncation, for a number of state-of-the-art DGNs. We also present
quantitative and qualitative results on the improvement of overall generation
quality (e.g., in terms of the Frechet Inception Distance) for a number of
state-of-the-art DGNs, including StyleGAN3, BigGAN-deep, NVAE, for different
conditional and unconditional image generation tasks. In particular, Polarity
Sampling redefines the state-of-the-art for StyleGAN2 on the FFHQ Dataset to
FID 2.57, StyleGAN2 on the LSUN Car Dataset to FID 2.27 and StyleGAN3 on the
AFHQv2 Dataset to FID 3.95. Demo: bit.ly/polarity-samp
