  The family of f-divergences is ubiquitously applied to generative modeling in
order to adapt the distribution of the model to that of the data.
Well-definedness of f-divergences, however, requires the distributions of the
data and model to overlap completely in every time step of training. As a
result, as soon as the support of distributions of data and model contain
non-overlapping portions, gradient based training of the corresponding model
becomes hopeless. Recent advances in generative modeling are full of remedies
for handling this support mismatch problem: key ideas include either modifying
the objective function to integral probability measures (IPMs) that are
well-behaved even on disjoint probabilities, or optimizing a well-behaved
variational lower bound instead of the true objective. We, on the other hand,
establish that a complete change of the objective function is unnecessary, and
instead an augmentation of the base measure of the problematic divergence can
resolve the issue. Based on this observation, we propose a generative model
which leverages the class of Scaled Bregman Divergences and generalizes both
f-divergences and Bregman divergences. We analyze this class of divergences and
show that with the appropriate choice of base measure it can resolve the
support mismatch problem and incorporate geometric information. Finally, we
study the performance of the proposed method and demonstrate promising results
on MNIST, CelebA and CIFAR-10 datasets.
