The covariance for clean data given a noisy observation is an important quantity in many training-free guided generation methods for diffusion models. Current methods require heavy test-time computation, altering the standard diffusion training process or denoiser architecture, or making heavy approximations. We propose a new framework that sidesteps these issues by using covariance information that is available for free from training data and the curvature of the generative trajectory, which is linked to the covariance through the second-order Tweedie's formula. We integrate these sources of information using (i) a novel method to transfer covariance estimates across noise levels and (ii) low-rank updates in a given noise level. We validate the method on linear inverse problems, where it outperforms recent baselines, especially with fewer diffusion steps.

翻译：在扩散模型的许多无需训练引导生成方法中，给定噪声观测条件下干净数据的协方差是一个重要量。现有方法需要繁重的测试时计算、改变标准扩散训练过程或去噪器架构，或进行大量近似。我们提出一个新框架，通过利用训练数据中免费可得的协方差信息以及生成轨迹的曲率（通过二阶Tweedie公式与协方差关联）来规避这些问题。我们通过以下方式整合这些信息源：（i）一种在噪声水平间传递协方差估计的新方法；（ii）在给定噪声水平下的低秩更新。我们在线性逆问题上验证了该方法，其性能优于近期基线方法，尤其在扩散步骤较少时表现更佳。