# An Iteration-Free Fixed-Point Estimator for Diffusion Inversion

arXiv: https://arxiv.org/abs/2512.08547 · HTML: https://mlsanity.com/paper/2512.08547/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 40 of its 45 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 40)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022)
- [MasaCtrl: Tuning-Free Mutual Self-Attention Control for Consistent Image Synthesis and Editing](https://mlsanity.com/paper/2304.08465/) (2023)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Zero-shot Image-to-Image Translation](https://mlsanity.com/paper/2302.03027/) (2023)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [nocaps: novel object captioning at scale](https://mlsanity.com/paper/1812.08658/) (2018)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [EDICT: Exact Diffusion Inversion via Coupled Transformations](https://mlsanity.com/paper/2211.12446/) (2022)
- [Style Injection in Diffusion: A Training-free Approach for Adapting Large-scale Diffusion Models for Style Transfer](https://mlsanity.com/paper/2312.09008/) (2023)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [ReNoise: Real Image Inversion Through Iterative Noising](https://mlsanity.com/paper/2403.14602/) (2024)
- [Elucidating the Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2308.15321/) (2023)
- [Prompt Tuning Inversion for Text-Driven Image Editing Using Diffusion Models](https://mlsanity.com/paper/2305.04441/) (2023)
- [Golden Noise for Diffusion Models: A Learning Framework](https://mlsanity.com/paper/2411.09502/) (2024)
- [Effective Real Image Editing with Accelerated Iterative Diffusion Inversion](https://mlsanity.com/paper/2309.04907/) (2023)

## Abstract (arXiv)

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.