# SAIP: A Plug-and-Play Scale-adaptive Module in Diffusion-based Inverse Problems

arXiv: https://arxiv.org/abs/2509.24580 · HTML: https://mlsanity.com/paper/2509.24580/

## Key facts

- Cited by 1 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 20 of its 28 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Placed in

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

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review](https://mlsanity.com/paper/2501.09685/) (2025)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [CFG-Zero*: Improved Classifier-Free Guidance for Flow Matching Models](https://mlsanity.com/paper/2503.18886/) (2025)
- [Variational Diffusion Posterior Sampling with Midpoint Guidance](https://mlsanity.com/paper/2410.09945/) (2024)
- [Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior](https://mlsanity.com/paper/2501.18913/) (2025)
- [A Mixture-Based Framework for Guiding Diffusion Models](https://mlsanity.com/paper/2502.03332/) (2025)
- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [Diffusion State-Guided Projected Gradient for Inverse Problems](https://mlsanity.com/paper/2410.03463/) (2024)

## Built on by (most cited first, 1 of 1)

- [Getting Your Guidance Weights Right in diffusion and flow-matching posterior sampling](https://mlsanity.com/paper/2610.03503/) (2026)

## Abstract (arXiv)

Solving inverse problems with diffusion models has shown promise in tasks such as image restoration. A common approach is to formulate the problem in a Bayesian framework and sample from the posterior by combining the prior score with the likelihood score. Since the likelihood term is often intractable, estimators like DPS, DMPS, and πGDM are widely adopted. However, these methods rely on a fixed, manually tuned scale to balance prior and likelihood contributions. Such a static design is suboptimal, as the ideal balance varies across timesteps and tasks, limiting performance and generalization. To address this issue, we propose SAIP, a plug-and-play module that adaptively refines the scale at each timestep without retraining or altering the diffusion backbone. SAIP integrates seamlessly into existing samplers and consistently improves reconstruction quality across diverse image restoration tasks, including challenging scenarios.