  This paper considers the general $f$-divergence formulation of bidirectional
generative modeling, which includes VAE and BiGAN as special cases. We present
a new optimization method for this formulation, where the gradient is computed
using an adversarially learned discriminator. In our framework, we show that
different divergences induce similar algorithms in terms of gradient
evaluation, except with different scaling. Therefore this paper gives a general
recipe for a class of principled $f$-divergence based generative modeling
methods. Theoretical justifications and extensive empirical studies are
provided to demonstrate the advantage of our approach over existing methods.
