On Exact Inversion of DPM-Solvers

Diffusion probabilistic models (DPMs) are a key component in modern generative models. DPM-solvers have achieved reduced latency and enhanced quality signifi-cantly, but have posed challenges to find the exact inverse (i.e., finding the initial noise from the given image). Here we investigate the exact inversions for DPM-solvers and pro-pose algorithms to perform them when samples are gener-ated by the first-order as well as higher-order DPM-solvers. For each explicit denoising step in DPM-solvers, we formu-lated the inversions using implicit methods such as gradi-ent descent or forward step method to ensure the robustness to large classifier-free guidance unlike the prior approach using fixed-point iteration. Experimental results demon-strated that our proposed exact inversion methods signif-icantly reduced the error of both image and noise reconstructions, greatly enhanced the ability to distinguish invis-ible watermarks and well prevented unintended background changes consistently during image editing.