# SSI-DM: Singularity Skipping Inversion of Diffusion Models

arXiv: https://arxiv.org/abs/2602.02193 · HTML: https://mlsanity.com/paper/2602.02193/

## 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 36 of its 45 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## 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 36)

- [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)
- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022)
- [DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulation](https://mlsanity.com/paper/2110.02711/) (2021)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Zero-shot Image-to-Image Translation](https://mlsanity.com/paper/2302.03027/) (2023)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [EDICT: Exact Diffusion Inversion via Coupled Transformations](https://mlsanity.com/paper/2211.12446/) (2022)
- [An Edit Friendly DDPM Noise Space: Inversion and Manipulations](https://mlsanity.com/paper/2304.06140/) (2023)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data](https://mlsanity.com/paper/2302.07194/) (2023)
- [Negative-prompt Inversion: Fast Image Inversion for Editing with Text-guided Diffusion Models](https://mlsanity.com/paper/2305.16807/) (2023)
- [LEDITS++: Limitless Image Editing using Text-to-Image Models](https://mlsanity.com/paper/2311.16711/) (2023)
- [ReNoise: Real Image Inversion Through Iterative Noising](https://mlsanity.com/paper/2403.14602/) (2024)
- [Score-Based Generative Models Detect Manifolds](https://mlsanity.com/paper/2206.01018/) (2022)
- [Prompt Tuning Inversion for Text-Driven Image Editing Using Diffusion Models](https://mlsanity.com/paper/2305.04441/) (2023)
- [Improving Tuning-Free Real Image Editing with Proximal Guidance](https://mlsanity.com/paper/2306.05414/) (2023)

## Abstract (arXiv)

Inverting real images into the noise space is essential for editing tasks using diffusion models, yet existing methods produce non-Gaussian noise with poor editability due to the inaccuracy in early noising steps. We identify the root cause: a mathematical singularity that renders inversion fundamentally ill-posed. We propose Singularity Skipping Inversion of Diffusion Models (SSI-DM), which bypasses this singular region by adding small noise before standard inversion. This simple approach produces inverted noise with natural Gaussian properties while maintaining reconstruction fidelity. As a plug-and-play technique compatible with general diffusion models, our method achieves superior performance on public image datasets for reconstruction and interpolation tasks, providing a principled and efficient solution to diffusion model inversion.