  The Schr\"odinger Bridge (SB) problem offers a powerful framework for
combining optimal transport and diffusion models. A promising recent approach
to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure,
which alternates between Markovian and reciprocal projections of
continuous-time stochastic processes. However, the model built by the IMF
procedure has a long inference time due to using many steps of numerical
solvers for stochastic differential equations. To address this limitation, we
propose a novel Discrete-time IMF (D-IMF) procedure in which learning of
stochastic processes is replaced by learning just a few transition
probabilities in discrete time. Its great advantage is that in practice it can
be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already
well-established adversarial generative modeling technique. We show that our
D-IMF procedure can provide the same quality of unpaired domain translation as
the IMF, using only several generation steps instead of hundreds.
