论文标题
基于小波得分的生成建模
Wavelet Score-Based Generative Modeling
论文作者
论文摘要
基于得分的生成模型（SGMS）通过运行时间转移的随机微分方程（SDE）从高斯白噪声中综合了新数据样本，其漂移系数取决于某些概率分数。此类SDE的离散化通常需要大量的时间步骤，因此需要高计算成本。这是因为我们通过数学分析的分数的不良条件特性。我们表明，通过将数据分布分配到跨尺度的小波系数的条件概率的产物中，SGM可以大大加速。所得的基于小波得分的生成模型（WSGM）在所有尺度上都以相同的时间步长合成小波系数，因此其时间复杂性随图像大小而线性增长。这在数学上是在高斯分布上证明的，并在相变和自然图像数据集中的物理过程上以数字显示。
Score-based generative models (SGMs) synthesize new data samples from Gaussian white noise by running a time-reversed Stochastic Differential Equation (SDE) whose drift coefficient depends on some probabilistic score. The discretization of such SDEs typically requires a large number of time steps and hence a high computational cost. This is because of ill-conditioning properties of the score that we analyze mathematically. We show that SGMs can be considerably accelerated, by factorizing the data distribution into a product of conditional probabilities of wavelet coefficients across scales. The resulting Wavelet Score-based Generative Model (WSGM) synthesizes wavelet coefficients with the same number of time steps at all scales, and its time complexity therefore grows linearly with the image size. This is proved mathematically over Gaussian distributions, and shown numerically over physical processes at phase transition and natural image datasets.
