# POLARIS: Projection-Orthogonal Least Squares for Robust and Adaptive Inversion in Diffusion Models

arXiv: https://arxiv.org/abs/2512.00369 · HTML: https://mlsanity.com/paper/2512.00369/

## Key facts

- Cited by 8 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 29 of its 36 references that are in the map.
- First posted on arXiv 29 Nov 2025.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [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)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [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)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022)
- [MasaCtrl: Tuning-Free Mutual Self-Attention Control for Consistent Image Synthesis and Editing](https://mlsanity.com/paper/2304.08465/) (2023)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Paint by Example: Exemplar-based Image Editing with Diffusion Models](https://mlsanity.com/paper/2211.13227/) (2022)
- [Blended Latent Diffusion](https://mlsanity.com/paper/2206.02779/) (2022)
- [EDICT: Exact Diffusion Inversion via Coupled Transformations](https://mlsanity.com/paper/2211.12446/) (2022)
- [Negative-prompt Inversion: Fast Image Inversion for Editing with Text-guided Diffusion Models](https://mlsanity.com/paper/2305.16807/) (2023)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [Direct Inversion: Boosting Diffusion-based Editing with 3 Lines of Code](https://mlsanity.com/paper/2310.01506/) (2023)
- [Prompt Tuning Inversion for Text-Driven Image Editing Using Diffusion Models](https://mlsanity.com/paper/2305.04441/) (2023)
- [A Formal Evaluation of PSNR as Quality Measurement Parameter for Image Segmentation Algorithms](https://mlsanity.com/paper/1605.07116/) (2016)
- [Lightning-Fast Image Inversion and Editing for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2312.12540/) (2023)
- [DCTdiff: Intriguing Properties of Image Generative Modeling in the DCT Space](https://mlsanity.com/paper/2412.15032/) (2024)
- [BELM: Bidirectional Explicit Linear Multi-step Sampler for Exact Inversion in Diffusion Models](https://mlsanity.com/paper/2410.07273/) (2024)
- [Noise Map Guidance: Inversion with Spatial Context for Real Image Editing](https://mlsanity.com/paper/2402.04625/) (2024)
- [ANT: Adaptive Neural Temporal-Aware Text-to-Motion Model](https://mlsanity.com/paper/2506.02452/) (2025)
- [Don't Forget your Inverse DDIM for Image Editing](https://mlsanity.com/paper/2505.09571/) (2025)

## Built on by (most cited first, 8 of 8)

- [ECHO: Edge-Cloud Humanoid Orchestration for Language-to-Motion Control](https://mlsanity.com/paper/2603.16188/) (2026)
- [Oracle Noise: Faster Semantic Spherical Alignment for Interpretable Latent Optimization](https://mlsanity.com/paper/2604.23540/) (2026)
- [AnyEdit++: Adaptive Long-Form Knowledge Editing via Bayesian Surprise](https://mlsanity.com/paper/2606.01053/) (2026)
- [Z2-Sampling: Zero-Cost Zigzag Trajectories for Semantic Alignment in Diffusion Models](https://mlsanity.com/paper/2604.23536/) (2026)
- [When Does High-CFG Diffusion Inversion Fail? A Controlled Study of Prompt--Latent Interactions](https://mlsanity.com/paper/2607.04731/) (2026)
- [Before the Body Moves: Learning Anticipatory Joint Intent for Language-Conditioned Humanoid Control](https://mlsanity.com/paper/2605.14417/) (2026)
- [Learning to Think in Physics: Breaking Shortcut Learning in Scientific Diffusion via Representation Alignment](https://mlsanity.com/paper/2605.20780/) (2026)
- [GeoShrink: Accelerating Diffusion Transformers with Two Lines of Code](https://mlsanity.com/paper/2609.33723/) (2026)

## Abstract (arXiv)

The Inversion-Denoising Paradigm, which is based on diffusion models, excels in diverse image editing and restoration tasks. We revisit its mechanism and reveal a critical, overlooked factor in reconstruction degradation: the approximate noise error. This error stems from approximating the noise at step t with the prediction at step t-1, resulting in severe error accumulation throughout the inversion process. We introduce Projection-Orthogonal Least Squares for Robust and Adaptive Inversion (POLARIS), which reformulates inversion from an error-compensation problem into an error-origin problem. Rather than optimizing embeddings or latent codes to offset accumulated drift, POLARIS treats the guidance scale ω as a step-wise variable and derives a mathematically grounded formula to minimize inversion error at each step. Remarkably, POLARIS improves inversion latent quality with just one line of code. With negligible performance overhead, it substantially mitigates noise approximation errors and consistently improves the accuracy of downstream tasks.