Recent diffusion-based generative models achieve remarkable results by training on massive datasets, yet this practice raises concerns about memorization and copyright infringement. A proposed remedy is to train exclusively on noisy data with potential copyright issues, ensuring the model never observes original content. However, through the lens of deconvolution theory, we show that although it is theoretically feasible to learn the data distribution from noisy samples, the practical challenge of collecting sufficient samples makes successful learning nearly unattainable. To overcome this limitation, we propose to pretrain the model with a small fraction of clean data to guide the deconvolution process. Combined with our Stochastic Forward--Backward Deconvolution (SFBD) method, we attain an FID of $6.31$ on CIFAR-10 with just $4\%$ clean images (and $3.58$ with $10\%$). Theoretically, we prove that SFBD guides the model to learn the true data distribution. The result also highlights the importance of pretraining on limited but clean data or the alternative from similar datasets. Empirical studies further support these findings and offer additional insights.

Audio classification is considered as a challenging problem in pattern recognition. Recently, many algorithms have been proposed using deep neural networks. In this paper, we introduce a new attention-based neural network architecture called Classifier-Attention-Based Convolutional Neural Network (CAB-CNN). The algorithm uses a newly designed architecture consisting of a list of simple classifiers and an attention mechanism as a classifier selector. This design significantly reduces the number of parameters required by the classifiers and thus their complexities. In this way, it becomes easier to train the classifiers and achieve a high and steady performance. Our claims are corroborated by the experimental results. Compared to the state-of-the-art algorithms, our algorithm achieves more than 10% improvements on all selected test scores.