Recent advance in score-based models incorporates the stochastic differential equation (SDE), which brings the state-of-the art performance on image generation tasks. This paper improves such score-based models by analyzing the model at the zero perturbation noise. In real datasets, the score function diverges as the perturbation noise ($\sigma$) decreases to zero, and this observation leads an argument that the score estimation fails at $\sigma=0$ with any neural network structure. Subsequently, we introduce Unbounded Noise Conditional Score Network (UNCSN) that resolves the score diverging problem with an easily applicable modification to any noise conditional score-based models. Additionally, we introduce a new type of SDE, so the exact log likelihood can be calculated from the newly suggested SDE. On top of that, the associated loss function mitigates the loss imbalance issue in a mini-batch, and we present a theoretic analysis on the proposed loss to uncover the behind mechanism of the data distribution modeling by the score-based models.

中文翻译：

---

无界数据评分的评分匹配模型

基于分数的模型的最新进展结合了随机微分方程 (SDE)，它为图像生成任务带来了最先进的性能。本文通过在零扰动噪声下分析模型来改进这种基于分数的模型。在实际数据集中，分数函数随着扰动噪声 ($\sigma$) 减小到零而发散，并且这种观察导致了这样的论点：对于任何神经网络结构，分数估计在 $\sigma=0$ 时都失败了。随后，我们引入了无界噪声条件评分网络 (UNCSN)，该网络通过对任何基于噪声条件评分的模型进行简单适用的修改来解决评分发散问题。此外，我们引入了一种新型 SDE，因此可以根据新建议的 SDE 计算精确的对数似然。最重要的是，