Constructing fast samplers for unconditional diffusion and flow-matching models has received much attention recently; however, existing methods for solving inverse problems, such as super-resolution, inpainting, or deblurring, still require hundreds to thousands of iterative steps to obtain high-quality results. We propose a plug-and-play framework for constructing efficient samplers for inverse problems, requiring only pre-trained diffusion or flow-matching models. We present Conditional Conjugate Integrators, which leverage the specific form of the inverse problem to project the respective conditional diffusion/flow dynamics into a more amenable space for sampling. Our method complements popular posterior approximation methods for solving inverse problems using diffusion/flow models. We evaluate the proposed method's performance on various linear image restoration tasks across multiple datasets, employing diffusion and flow-matching models. Notably, on challenging inverse problems like 4x super-resolution on the ImageNet dataset, our method can generate high-quality samples in as few as 5 conditional sampling steps and outperforms competing baselines requiring 20-1000 steps. Our code will be publicly available at https://github.com/mandt-lab/c-pigdm

翻译：为无条件扩散模型和流匹配模型构建快速采样器近来备受关注；然而，现有方法在解决超分辨率、修复或去模糊等逆问题时，仍需要数百至数千次迭代步骤才能获得高质量结果。我们提出一种即插即用框架，用于构建逆问题的高效采样器，仅需预训练的扩散或流匹配模型。我们提出条件共轭积分器，该方法利用逆问题的特定形式，将相应的条件扩散/流动力学投影到更易于采样的空间中。我们的方法补充了使用扩散/流模型解决逆问题时常用的后验近似方法。我们在多个数据集上，针对各类线性图像复原任务，采用扩散和流匹配模型评估了所提方法的性能。值得注意的是，在ImageNet数据集上进行4倍超分辨率等具有挑战性的逆问题时，我们的方法仅需5个条件采样步骤即可生成高质量样本，且性能优于需要20-1000步的基线方法。代码将在https://github.com/mandt-lab/c-pigdm 公开。