Compression Asymmetry and Trajectory Binding in Noise-Anchored Diffusion Inversion

2026-07-08

AI Summary

This work addresses the trade-off between reconstruction quality and computational/storage costs in solving real-image diffusion inverse problems by proposing NARC, a training-free, efficient inverse mapping method. NARC leverages diffusion trajectories defined by forward Gaussian noise anchors and exploits two key properties of these anchors: element-wise compression asymmetry and trajectory binding. By employing a single int8-quantized latent anchor and noise-level-dependent weighting schedules, NARC achieves high-fidelity reconstructions with drastically reduced overhead. Evaluated on PIE-Bench++, the method improves PSNR by 3.24 dB over PnP DirectInv when applied to Stable Diffusion 1.5, while reducing storage requirements by approximately 400×. Furthermore, NARC successfully scales to SDXL at 1024² resolution, demonstrating its effectiveness and versatility across model architectures and image sizes.

Abstract

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.

Problem

• diffusion inversion
• compression asymmetry
• noise anchor
• trajectory binding
• storage-cost trade-off

Innovation

• compression asymmetry
• trajectory binding
• noise-anchored inversion
• training-free inversion
• diffusion reconstruction