  Recent years have seen the rise of convolutional neural network techniques in
exemplar-based image synthesis. These methods often rely on the minimization of
some variational formulation on the image space for which the minimizers are
assumed to be the solutions of the synthesis problem. In this paper we
investigate, both theoretically and experimentally, another framework to deal
with this problem using an alternate sampling/minimization scheme. First, we
use results from information geometry to assess that our method yields a
probability measure which has maximum entropy under some constraints in
expectation. Then, we turn to the analysis of our method and we show, using
recent results from the Markov chain literature, that its error can be
explicitly bounded with constants which depend polynomially in the dimension
even in the non-convex setting. This includes the case where the constraints
are defined via a differentiable neural network. Finally, we present an
extensive experimental study of the model, including a comparison with
state-of-the-art methods and an extension to style transfer.
