# There and Back Again: On the relation between Noise and Image Inversions in Diffusion Models

arXiv: https://arxiv.org/abs/2410.23530 · HTML: https://mlsanity.com/paper/2410.23530/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 8 of its 75 references that are in the map.
- First posted on arXiv 31 Oct 2024.

## Placed in

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

## Builds on (most cited first, 8 of 8)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Dual Diffusion Implicit Bridges for Image-to-Image Translation](https://mlsanity.com/paper/2203.08382/) (2022)
- [Negative-prompt Inversion: Fast Image Inversion for Editing with Text-guided Diffusion Models](https://mlsanity.com/paper/2305.16807/) (2023)
- [Understanding DDPM Latent Codes Through Optimal Transport](https://mlsanity.com/paper/2202.07477/) (2022)
- [Schedule Your Edit: A Simple yet Effective Diffusion Noise Schedule for Image Editing](https://mlsanity.com/paper/2410.18756/) (2024)
- [BELM: Bidirectional Explicit Linear Multi-step Sampler for Exact Inversion in Diffusion Models](https://mlsanity.com/paper/2410.07273/) (2024)

## Built on by (most cited first, 1 of 1)

- [FARI: Robust One-Step Inversion for Watermarking in Diffusion Models](https://mlsanity.com/paper/2607.26723/) (2026)

## Abstract (arXiv)

Diffusion Models achieve state-of-the-art performance in generating new samples but lack a low-dimensional latent space that encodes the data into editable features. Inversion-based methods address this by reversing the denoising trajectory, transferring images to their approximated starting noise. In this work, we thoroughly analyze this procedure and focus on the relation between the initial noise, the generated samples, and their corresponding latent encodings obtained through the DDIM inversion. First, we show that latents exhibit structural patterns in the form of less diverse noise predicted for smooth image areas (e.g., plain sky). Through a series of analyses, we trace this issue to the first inversion steps, which fail to provide accurate and diverse noise. Consequently, the DDIM inversion space is notably less manipulative than the original noise. We show that prior inversion methods do not fully resolve this issue, but our simple fix, where we replace the first DDIM Inversion steps with a forward diffusion process, successfully decorrelates latent encodings and enables higher quality editions and interpolations. The code is available at https://github.com/luk-st/taba.