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 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：本文提出信息-估计度量（IEM），这是一种从信号域上的连续概率密度函数推导出的新型距离函数。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关联。具体而言，一对信号间的IEM是通过比较它们在噪声幅度范围内的去噪误差向量获得的。从几何角度看，这等价于比较不同模糊程度下信号周围模糊密度函数的得分向量场。我们证明了IEM是有效的全局度量，并推导出其局部二阶近似的闭式表达式，从而得到黎曼度量。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，它能从局部和全局两个层面自适应地匹配分布的几何特性。在实际应用中，IEM可通过使用训练好的去噪器（类似于生成扩散模型）并求解一维积分来计算。为验证本框架的价值，我们在ImageNet数据库上训练了IEM。实验表明，在预测人类感知判断方面，该IEM与当前最先进的监督式图像质量度量方法相比具有竞争力甚至表现更优。