計分式生成模型（Score-based Generative Modeling）是目前生成模型當中生成品質最佳的技術之一，在這樣的模型中我們依照對數後的概率密度函數(Probability Density Function)之梯度做資料生成，本文探討計分式生成模型在引入條件式生成之框架下的困難之處與解決方法。
許多現有的條件計分式生成模型利用貝氏定理將對數後的事後概率密度函數（Posterior Probability Density Function）之梯度分解為計分函數與概似計分函數。這些方法促進了條件計分式模型之訓練過程，因為可以使用計分式模型和分類器的輸出之和去估計對數後的事後概率密度函數之梯度。然而，此論文的分析表明這些方法中分類器的訓練目標可能會導致嚴重的分數不匹配問題，這表示估計的概似計分函數偏離真實的概似計分函數的情況。這種問題會導致在擴散採樣的過程中，樣本被錯誤的計分函數誤導，從而導致採樣質量下降。為了解決這個問題，我們提出了一種新的訓練方法，稱為降噪概似計分匹配（Denoising Likelihood Score Matching），用於使分類器的梯度匹配真實概似計分函數。此論文的實驗證據表明，所提出的方法在 CIFAR-10 和 CIFAR-100 資料集測試中明顯優於先前的方法。因此，此論文得出結論：通過採用降噪概似計分匹配，可以使分類器準確地估計概似計分函數，並減輕分數不匹配問題的影響。
此論文研究已被《國際表徵學習會議》（ICLR 2022）接受發表。

Many existing conditional score-based data generation methods utilize Bayes’ theorem to decompose the gradients of a log posterior density into a mixture of scores. These methods facilitate the training procedure of conditional score models, as a mixture of scores can be separately estimated using a score model and a classifier. However, our analysis indicates that the training objectives for the classifier in these methods may lead to a serious score mismatch issue, which corresponds to the situation that the estimated scores deviate from the true ones. Such an issue causes the samples to be misled by the deviated scores during the diffusion process, resulting in a degraded sampling quality. To resolve it, we theoretically formulate a novel training objective, called Denoising Likelihood Score Matching (DLSM) loss, for the classifier to match the gradients of the true log likelihood density. Our experimental evidences show that the proposed method outperforms the previous methods on both CIFAR-10 and CIFAR-100 datasets noticeably in terms of several key evaluation metrics. We thus conclude that, by adopting DLSM, the conditional scores can be accurately modeled, and the effect of the score mismatch issue is alleviated.
This research paper has been accepted by the International Conference on Learning Representations (ICLR 2022).

Abstract (Chinese) 1
Acknowledgements (Chinese) 2
Abstract 3
Acknowledgements 4
Contents 5
List of Figures 7
List of Tables 9
1. Introduction 10
2. Background 12
3. Analysis on the Score Mismatch Issue 17
4. Denoising Likelihood Score Matching 21
5. Experiments 25
6. Conclusion 30
Bibliography 31

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