Noise is All You Need: Solving Linear Inverse Problems by Noise Combination Sampling with Diffusion Models

TL;DR

This paper introduces Noise Combination Sampling, a novel diffusion model technique that improves inverse problem solving by synthesizing optimal noise vectors, enhancing robustness and stability without complex tuning.

Contribution

The paper proposes a new noise synthesis method for diffusion models that better incorporates measurement constraints in inverse problems, avoiding hyperparameter tuning.

Findings

Outperforms existing methods in image compression tasks.

Achieves superior robustness and stability with fewer generation steps.

Requires negligible additional computational overhead.

Abstract

Pretrained diffusion models have demonstrated strong capabilities in zero-shot inverse problem solving by incorporating observation information into the generation process of the diffusion models. However, this presents an inherent dilemma: excessive integration can disrupt the generative process, while insufficient integration fails to emphasize the constraints imposed by the inverse problem. To address this, we propose \emph{Noise Combination Sampling}, a novel method that synthesizes an optimal noise vector from a noise subspace to approximate the measurement score, replacing the noise term in the standard Denoising Diffusion Probabilistic Models process. This enables conditional information to be naturally embedded into the generation process without reliance on step-wise hyperparameter tuning. Our method can be applied to a wide range of inverse problem solvers, including image compression, and, particularly when the number of generation steps $T$ is small, achieves superior performance with negligible computational overhead, significantly improving robustness and stability.