无需导数信息，用扩散模型解决复杂逆问题
Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems
- 基于集合卡尔曼滤波，仅通过前向模型输出求解
- 在流体、天体等非线性逆问题中表现优异
- 适合无法获取梯度或模型结构的科学计算场景
求解逆问题时，使用预训练扩散模型作为即插即用先验的方法日益流行。该框架可适应不同前向模型而无需重新训练，同时保持扩散模型的生成能力。尽管在众多成像逆问题中取得成功，现有方法大多依赖导数、伪逆或对前向模型的完整知识，这在许多科学应用中难以获得，成为主要限制。我们提出无需导数的集合卡尔曼扩散引导（EnKG）方法，仅需前向模型评估和预训练扩散模型先验即可求解逆问题。我们在多种逆问题上验证了EnKG的实证有效性，包括流体流动和天体物体推断等高度非线性的科学场景，这些场景通常只能以黑盒形式访问前向模型。代码已开源：https://github.com/devzhk/enkg-pytorch。
原文摘要 · Abstract (English)
When solving inverse problems, one increasingly popular approach is 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. We propose Ensemble Kalman Diffusion Guidance (EnKG), 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 EnKG 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. We open-source our code at https://github.com/devzhk/enkg-pytorch.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。