Conditional Simulation Using Diffusion Schrödinger Bridges
Yuyang Shi Department of Statistics University of Oxford, UK Valentin De Bortoli ENS, PSL University, Paris, France George Deligiannidis Department of Statistics University of Oxford, UK Arnaud Doucet Department of Statistics University of Oxford, UK
Abstract
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.
中文速览
扩散生成模型（Score-Based Generative Models）效果出色，但生成时需要跑很长的扩散链，速度慢是其硬伤；薛定谔桥（Schrödinger Bridge）方法此前已被证明能在无条件生成场景下大幅缩短扩散步数，但还没有人把它推广到条件生成（即已知观测值 y 后从后验分布采样）这一更实用的场景。本文提出条件扩散薛定谔桥（Conditional Diffusion Schrödinger Bridge, CDSB），将薛定谔桥的迭代比例拟合框架扩展到条件模拟，通过训练一对神经网络交替逼近前向与后向的条件转移概率，从而在更短的扩散链上实现高质量的后验采样。实验覆盖图像超分辨率、状态空间模型的最优滤波（这也是分数匹配方法在该任务上的首次应用）以及预训练网络的输出精修等多个任务，均验证了方法的有效性。这一工作填补了薛定谔桥在条件生成领域的空白，为需要快速、准确后验推断的实际逆问题提供了一条有理论支撑的新路径。
原文 arXiv:2202.13460;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2202.13460v2