Diffusion probabilistic models have been successfully used to generate data from noise. However, most diffusion models are computationally expensive and difficult to interpret with a lack of theoretical justification. Random feature models on the other hand have gained popularity due to their interpretability but their application to complex machine learning tasks remains limited. In this work, we present a diffusion model-inspired deep random feature model that is interpretable and gives comparable numerical results to a fully connected neural network having the same number of trainable parameters. Specifically, we extend existing results for random features and derive generalization bounds between the distribution of sampled data and the true distribution using properties of score matching. We validate our findings by generating samples on the fashion MNIST dataset and instrumental audio data.

翻译：扩散概率模型已被成功用于从噪声中生成数据。然而，大多数扩散模型计算成本高昂且缺乏理论支撑导致难以解释。另一方面，随机特征模型因其可解释性而备受关注，但其在复杂机器学习任务中的应用仍十分有限。本文提出了一种受扩散模型启发的深度随机特征模型，该模型具有可解释性，并在与具有相同可训练参数数量的全连接神经网络相比时，可获得相当数值结果。具体而言，我们扩展了现有随机特征理论，利用分数匹配的性质推导了采样数据分布与真实分布之间的泛化界。通过在Fashion MNIST数据集和乐器音频数据上生成样本，我们验证了该方法的有效性。