  We propose to learn a generative model via entropy interpolation with a
Schr\"{o}dinger Bridge. The generative learning task can be formulated as
interpolating between a reference distribution and a target distribution based
on the Kullback-Leibler divergence. At the population level, this entropy
interpolation is characterized via an SDE on $[0,1]$ with a time-varying drift
term. At the sample level, we derive our Schr\"{o}dinger Bridge algorithm by
plugging the drift term estimated by a deep score estimator and a deep density
ratio estimator into the Euler-Maruyama method. Under some mild smoothness
assumptions of the target distribution, we prove the consistency of both the
score estimator and the density ratio estimator, and then establish the
consistency of the proposed Schr\"{o}dinger Bridge approach. Our theoretical
results guarantee that the distribution learned by our approach converges to
the target distribution. Experimental results on multimodal synthetic data and
benchmark data support our theoretical findings and indicate that the
generative model via Schr\"{o}dinger Bridge is comparable with state-of-the-art
GANs, suggesting a new formulation of generative learning. We demonstrate its
usefulness in image interpolation and image inpainting.
