  Image restoration, which aims to recover high-quality images from their
corrupted counterparts, often faces the challenge of being an ill-posed problem
that allows multiple solutions for a single input. However, most deep learning
based works simply employ l1 loss to train their network in a deterministic
way, resulting in over-smoothed predictions with inferior perceptual quality.
In this work, we propose a novel method that shifts the focus from a
deterministic pixel-by-pixel comparison to a statistical perspective,
emphasizing the learning of distributions rather than individual pixel values.
The core idea is to introduce spatial entropy into the loss function to measure
the distribution difference between predictions and targets. To make this
spatial entropy differentiable, we employ kernel density estimation (KDE) to
approximate the probabilities for specific intensity values of each pixel with
their neighbor areas. Specifically, we equip the entropy with diffusion models
and aim for superior accuracy and enhanced perceptual quality over l1 based
noise matching loss. In the experiments, we evaluate the proposed method for
low light enhancement on two datasets and the NTIRE challenge 2024. All these
results illustrate the effectiveness of our statistic-based entropy loss. Code
is available at https://github.com/shermanlian/spatial-entropy-loss.
