Abstract
Inverse problems (IPs) involve reconstructing signals from noisy observations. Traditional approaches often rely on handcrafted priors, which can fail to capture the complexity of real-world data. The advent of pre-trained generative models has introduced new paradigms, offering improved reconstructions by learning rich priors from data. Among these, diffusion models (DMs) have emerged as a powerful framework, achieving remarkable reconstruction performance across numerous IPs. However, existing DM-based methods frequently encounter issues such as heavy computational demands and suboptimal convergence. In this work, building upon the idea of the recent work DMPlug~\cite{wang2024dmplug}, we propose two novel methods, DMILO and DMILO-PGD, to address these challenges. Our first method, DMILO, employs intermediate layer optimization (ILO) to alleviate the memory burden inherent in DMPlug. Additionally, by introducing sparse deviations, we expand the range of DMs, enabling the exploration of underlying signals that may lie outside the range of the diffusion model. We further propose DMILO-PGD, which integrates ILO with projected gradient descent (PGD), thereby reducing the risk of suboptimal convergence. We provide an intuitive theoretical analysis of our approach under appropriate conditions and validate its superiority through extensive experiments on diverse image datasets, encompassing both linear and nonlinear IPs. Our results demonstrate significant performance gains over state-of-the-art methods, highlighting the effectiveness of DMILO and DMILO-PGD in addressing common challenges in DM-based IP solvers.
Abstract (translated)
逆向问题（IPs）涉及从含有噪声的观测数据中重构信号。传统的处理方法通常依赖于人工设计的先验知识，这些先验往往难以捕捉到现实世界数据中的复杂性。随着预训练生成模型的出现，新的范例被引入，通过从大量数据中学得更丰富的先验信息来改进重建效果。在这些方法中，扩散模型（DMs）作为一种强大的框架脱颖而出，在众多逆向问题上取得了显著的重构性能。然而，现有的基于扩散模型的方法常常会遇到计算需求重和次优收敛的问题。 在此项工作中，我们借鉴最近的工作 DMPlug~\cite{wang2024dmplug} 的思想，提出了两种新的方法：DMILO 和 DMILO-PGD，以解决这些问题。我们的第一种方法 DMILO 使用中间层优化（ILO）来减轻 DMPlug 中固有的内存负担。通过引入稀疏偏差，我们扩展了扩散模型的应用范围，使其能够探索可能超出扩散模型范围内底层信号的可能性。进一步地，我们提出了DMILO-PGD 方法，它将 ILO 与投影梯度下降（PGD）相结合，从而降低次优收敛的风险。 我们在适当的条件下对我们的方法进行了直观的理论分析，并通过在多种图像数据集上的广泛实验验证了其优越性，包括线性和非线性的逆向问题。我们的结果表明，在最先进的方法中取得了显著的性能提升，突显了 DMILO 和 DMILO-PGD 在基于扩散模型的逆向问题求解器中解决常见挑战的有效性。
URL
https://arxiv.org/abs/2505.20789
