Exact diffusion inversion via bi-directional integration approximation

Abstract

Recently, various methods have been proposed to address the inconsistency issue of DDIM inversion to enable image editing, such as EDICT and Null-text inversion. However, the above methods introduce considerable computational overhead. In this paper, we propose a new technique, bidirectional integration approximation (BDIA), to perform exact diffusion inversion with negligible computational overhead. We consider a family of second order integration algorithms obtained by averaging forward and backward DDIM steps. The resulting approach estimates the next diffusion state as a linear combination of the estimated Gaussian noise at the current step and the previous and current diffusion states. This allows for exact backward computation of previous state given the current and next ones, leading to exact diffusion inversion. We perform a convergence analysis for BDIA-DDIM that includes the analysis for DDIM as a special case. It is demonstrated with experiments that BDIA-DDIM is effective for (round-trip) prompt-driven image editing. Our experiments further show that BDIA-DDIM produces markedly better image sampling quality than DDIM and EDICT for text-to-image generation and conventional image sampling. BDIA can also be applied to improve the performance of other ODE solvers in addition to DDIM. In particular, it is found that applying BDIA to the EDM sampling procedure produces consistently better performance over four pre-trained models (see Alg. 4 and Table 3 in Appendix C).