  Denoising diffusion models have recently emerged as a powerful class of
generative models. They provide state-of-the-art results, not only for
unconditional simulation, but also when used to solve conditional simulation
problems arising in a wide range of inverse problems. A limitation of these
models is that they are computationally intensive at generation time as they
require simulating a diffusion process over a long time horizon. When
performing unconditional simulation, a Schr\"odinger bridge formulation of
generative modeling leads to a theoretically grounded algorithm shortening
generation time which is complementary to other proposed acceleration
techniques. We extend the Schr\"odinger bridge framework to conditional
simulation. We demonstrate this novel methodology on various applications
including image super-resolution, optimal filtering for state-space models and
the refinement of pre-trained networks. Our code can be found at
https://github.com/vdeborto/cdsb.
