Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

翻译：扩散模型已成为视觉领域中基础模型的关键支柱。其核心应用之一是通过单一扩散先验，无需针对每个任务重新训练，即可通用地解决不同的下游逆问题。大多数逆问题可以表述为在给定测量值（例如，掩码图像）的情况下推断数据（例如，完整图像）的后验分布。然而，这在扩散模型中具有挑战性，因为扩散过程的非线性和迭代特性使得后验难以处理。为应对这一挑战，我们提出一种变分方法，该方法通过设计力图近似真实后验分布。我们证明，我们的方法自然引出了去噪扩散过程的正则化（RED-Diff），其中不同时间步的降噪器同时对图像施加不同的结构约束。为衡量不同时间步降噪器的贡献，我们提出一种基于信噪比（SNR）的加权机制。我们的方法为利用扩散模型解决逆问题提供了新的变分视角，从而将采样形式化为随机优化，只需使用轻量级迭代即可直接应用现成求解器。我们在图像修复和超分辨率等图像恢复任务上的实验表明，与基于采样的最先进扩散模型相比，我们的方法具有优势。