用噪声组合采样让扩散模型更准地解逆问题。
Noise is All You Need: Solving Linear Inverse Problems by Noise Combination Sampling with Diffusion Models
- 从噪声子空间合成最优噪声，替代标准扩散模型中的噪声项。
- 小步数生成时性能显著提升，计算开销几乎为零。
- 无需调参即可自然融入条件信息，适合各类逆问题求解。
预训练扩散模型通过将观测信息融入生成过程，在零样本逆问题求解中表现出强大能力。然而这带来一个根本矛盾：过度融合会破坏生成过程，融合不足则无法有效施加逆问题约束。为此，我们提出「噪声组合采样」方法，从噪声子空间合成最优噪声向量以近似测量得分，替代标准去噪扩散概率模型中的噪声项。该方法使条件信息自然嵌入生成过程，无需逐步超参数调优。本方法适用于多种逆问题求解器，包括图像压缩；尤其在生成步数 $T$ 较小时，性能更优且计算开销可忽略，显著提升鲁棒性与稳定性。
原文摘要 · Abstract (English)
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.
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