An Iteration-Free Fixed-Point Estimator for Diffusion Inversion

TL;DR

This paper introduces an iteration-free fixed-point estimator for diffusion inversion that reduces computational costs and hyperparameter tuning, providing accurate image reconstruction without iterative procedures.

Contribution

The authors derive an explicit fixed point expression and develop an error approximation method, enabling efficient, unbiased diffusion inversion without iterative fixed-point procedures.

Findings

Achieves superior reconstruction performance compared to iterative methods.

Reduces computational costs and hyperparameter tuning.

Validated on NOCAPS and MS-COCO datasets.

Abstract

Diffusion inversion aims to recover the initial noise corresponding to a given image such that this noise can reconstruct the original image through the denoising diffusion process. The key component of diffusion inversion is to minimize errors at each inversion step, thereby mitigating cumulative inaccuracies. Recently, fixed-point iteration has emerged as a widely adopted approach to minimize reconstruction errors at each inversion step. However, it suffers from high computational costs due to its iterative nature and the complexity of hyperparameter selection. To address these issues, we propose an iteration-free fixed-point estimator for diffusion inversion. First, we derive an explicit expression of the fixed point from an ideal inversion step. Unfortunately, it inherently contains an unknown data prediction error. Building upon this, we introduce the error approximation, which uses the calculable error from the previous inversion step to approximate the unknown error at the current inversion step. This yields a calculable, approximate expression for the fixed point, which is an unbiased estimator characterized by low variance, as shown by our theoretical analysis. We evaluate reconstruction performance on two text-image datasets, NOCAPS and MS-COCO. Compared to DDIM inversion and other inversion methods based on the fixed-point iteration, our method achieves consistent and superior performance in reconstruction tasks without additional iterations or training.