BELM: Bidirectional Explicit Linear Multi-step Sampler for Exact Inversion in Diffusion Models Fangyikang Wang 1 Hubery Yin 2 Yuejiang Dong

The inversion of diffusion model sampling, which aims to find the corresponding initial noise of a sample, plays a critical role in various tasks. Recently, several heuristic exact inversion samplers have been proposed to address the inexact inversion issue in a training-free manner. However, the theoretical properties of these heuristic samplers remain unknown and they often exhibit mediocre sampling quality. In this paper, we introduce a generic formulation, Bidirectional Explicit Linear Multi-step (BELM) samplers, of the exact inversion samplers, which includes all previously proposed heuristic exact inversion samplers as special cases.