# Spectral Collapse in Diffusion Inversion

arXiv: https://arxiv.org/abs/2602.13303 · HTML: https://mlsanity.com/paper/2602.13303/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 24 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [EDICT: Exact Diffusion Inversion via Coupled Transformations](https://mlsanity.com/paper/2211.12446/) (2022)
- [Focal Frequency Loss for Image Reconstruction and Synthesis](https://mlsanity.com/paper/2012.12821/) (2020)
- [Negative-prompt Inversion: Fast Image Inversion for Editing with Text-guided Diffusion Models](https://mlsanity.com/paper/2305.16807/) (2023)
- [Direct Inversion: Boosting Diffusion-based Editing with 3 Lines of Code](https://mlsanity.com/paper/2310.01506/) (2023)
- [ReNoise: Real Image Inversion Through Iterative Noising](https://mlsanity.com/paper/2403.14602/) (2024)
- [Exact Diffusion Inversion via Bi-directional Integration Approximation](https://mlsanity.com/paper/2307.10829/) (2023)
- [Spectral Analysis of Diffusion Models with Application to Schedule Design](https://mlsanity.com/paper/2502.00180/) (2025)
- [Is Your Conditional Diffusion Model Actually Denoising?](https://mlsanity.com/paper/2512.18736/) (2025)

## Abstract (arXiv)

Conditional diffusion inversion provides a powerful framework for unpaired image-to-image translation. However, we demonstrate through an extensive analysis that standard deterministic inversion (e.g. DDIM) fails when the source domain is spectrally sparse compared to the target domain (e.g., super-resolution, sketch-to-image). In these contexts, the recovered latent from the input does not follow the expected isotropic Gaussian distribution. Instead it exhibits a signal with lower frequencies, locking target sampling to oversmoothed and texture-poor generations. We term this phenomenon spectral collapse. We observe that stochastic alternatives attempting to restore the noise variance tend to break the semantic link to the input, leading to structural drift. To resolve this structure-texture trade-off, we propose Orthogonal Variance Guidance (OVG), an inference-time method that corrects the ODE dynamics to enforce the theoretical Gaussian noise magnitude within the null-space of the structural gradient. Extensive experiments on microscopy super-resolution (BBBC021) and sketch-to-image (Edges2Shoes) demonstrate that OVG effectively restores photorealistic textures while preserving structural fidelity.