Exploring Fixed Point in Image Editing: Theoretical Support and Convergence Optimization

In image editing, Denoising Diffusion Implicit Models (DDIM) inversion has become a widely adopted method and is extensively used in various image editing approaches. The core concept of DDIM inversion stems from the deterministic sampling technique of DDIM, which allows the DDIM process to be viewed as an Ordinary Differential Equation (ODE) process that is reversible. This enables the prediction of corresponding noise from a reference image, ensuring that the restored image from this noise remains consistent with the reference image. Image editing exploits this property by modifying the cross-attention between text and images to edit specific objects while preserving the remaining regions. However, in the DDIM inversion, using the t 1 time step to approximate the noise prediction at time step t introduces errors between the restored image and the reference image.