When solving inverse problems, it is increasingly popular to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative capability of diffusion models. Despite their success in many imaging inverse problems, most existing methods rely on privileged information such as derivative, pseudo-inverse, or full knowledge about the forward model. This reliance poses a substantial limitation that restricts their use in a wide range of problems where such information is unavailable, such as in many scientific applications. To address this issue, we propose Ensemble Kalman Diffusion Guidance (EnKG) for diffusion models, a derivative-free approach that can solve inverse problems by only accessing forward model evaluations and a pre-trained diffusion model prior. We study the empirical effectiveness of our method across various inverse problems, including scientific settings such as inferring fluid flows and astronomical objects, which are highly non-linear inverse problems that often only permit black-box access to the forward model.

翻译：在求解反问题时，使用预训练的扩散模型作为即插即用先验正日益流行。该框架无需重新训练即可适应不同的前向模型，同时保持扩散模型的生成能力。尽管这些方法在许多成像反问题中取得了成功，但现有方法大多依赖于导数、伪逆或前向模型的完整知识等特权信息。这种依赖性构成了显著限制，使其无法广泛应用于此类信息不可得的问题，例如许多科学应用场景。为解决这一问题，我们提出了用于扩散模型的集成卡尔曼扩散引导（EnKG），这是一种仅需访问前向模型评估和预训练扩散模型先验即可求解反问题的无导数方法。我们通过多种反问题（包括推断流体流动和天文物体等科学场景）实证验证了本方法的有效性，这些高度非线性的反问题通常仅允许对前向模型进行黑盒访问。