# Compression Asymmetry and Trajectory Binding in Noise-Anchored Diffusion Inversion

arXiv: https://arxiv.org/abs/2607.09784 · HTML: https://mlsanity.com/paper/2607.09784/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 20 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Builds on (most cited first, 14 of 14)

- [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)
- [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)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [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)
- [An Edit Friendly DDPM Noise Space: Inversion and Manipulations](https://mlsanity.com/paper/2304.06140/) (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)
- [SwiftEdit: Lightning Fast Text-Guided Image Editing via One-Step Diffusion](https://mlsanity.com/paper/2412.04301/) (2024)
- [FreeInv: Free Lunch for Improving DDIM Inversion](https://mlsanity.com/paper/2503.23035/) (2025)
- [DCI: Dual-Conditional Inversion for Boosting Diffusion-Based Image Editing](https://mlsanity.com/paper/2506.02560/) (2025)

## Abstract (arXiv)

Real-image diffusion inversion is governed by a tight quality-cost trade-off, with costs incurred in computation, storage, or per-image optimization. We study this trade-off through the forward Gaussian noise anchor that defines a diffusion trajectory and isolate two mechanisms behind effective stored-noise inversion. First, diffusion noise exhibits an element-wise compression asymmetry: int8 full-dimensional anchors preserve reconstruction, whereas low-dimensional subspace summaries are much less reliable, often collapsing even at comparable or smaller payloads; the element-wise over subspace ordering persists across five stored-noise inversion methods. Second, inversion is trajectory-bound and score-prior coupled: the matched forward anchor and a trained score network are both necessary, arguing against a purely algebraic-identity explanation. Together, these findings specify what to store and how to use it. They lead to Noise-Anchored Reverse Correction (NARC), a training-free inversion primitive that stores a single int8 latent anchor and reuses it with a fixed, noise-level-dependent anchor-weight schedule: strong anchoring when the reverse trajectory is noise-dominated, then relaxed anchoring as image detail emerges. On PIE-Bench++ with Stable Diffusion 1.5, NARC outperforms five modern non-exact baselines and improves PSNR by +3.24 dB over PnP DirectInv while using about 400x less inversion storage than PnP DirectInv. The compression asymmetry, anchor specificity, and editing plug-in also transfer to SDXL 1024^2.