Conditional Simulation Using Diffusion Schrödinger Bridges
This work addresses a computational bottleneck for researchers and practitioners using diffusion models in inverse problems, though it is incremental as it builds on existing unconditional simulation methods.
The paper tackles the computational inefficiency of denoising diffusion models in conditional simulation tasks by extending the Schrödinger bridge framework to conditional simulation, demonstrating its application in image super-resolution, optimal filtering, and network refinement.
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 Schrödinger 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 Schrödinger 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.