We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their denoising error vectors over a range of noise amplitudes. Geometrically, this amounts to comparing the score vector fields of the blurred density around the signals over a range of blur levels. We prove that the IEM is a valid global distance metric and derive a closed-form expression for its local second-order approximation, which yields a Riemannian metric. For Gaussian-distributed signals, the IEM coincides with the Mahalanobis distance. But for more complex distributions, it adapts, both locally and globally, to the geometry of the distribution. In practice, the IEM can be computed using a learned denoiser (analogous to generative diffusion models) and solving a one-dimensional integral. To demonstrate the value of our framework, we learn an IEM on the ImageNet database. Experiments show that this IEM is competitive with or outperforms state-of-the-art supervised image quality metrics in predicting human perceptual judgments.

翻译：本文提出了一种新颖的距离函数形式——信息-估计度量（IEM），该度量源自信号域上的底层连续概率密度。IEM 植根于信息论与估计理论之间的基本关系，该关系将信号的对数概率与最优去噪器在信号含噪观测下的误差相联系。具体而言，一对信号之间的 IEM 是通过比较它们在一系列噪声幅度下的去噪误差向量而获得的。从几何角度看，这等价于比较在一系列模糊程度下，信号周围模糊密度对应的得分向量场。我们证明了 IEM 是一个有效的全局距离度量，并推导出其局部二阶近似的闭式表达式，该表达式产生一个黎曼度量。对于高斯分布信号，IEM 与马氏距离一致。但对于更复杂的分布，IEM 会在局部和全局上自适应地适应分布的几何结构。在实践中，IEM 可以通过使用一个学习到的去噪器（类似于生成扩散模型）并求解一维积分来计算。为了展示我们框架的价值，我们在 ImageNet 数据库上学习了一个 IEM。实验表明，在预测人类感知判断方面，该 IEM 与最先进的监督式图像质量度量相比具有竞争力或表现更优。