Score-based generative modeling has recently emerged as a promising alternative to traditional likelihood-based or implicit approaches. Learning in score-based models involves first perturbing data with a continuous-time stochastic process, and then matching the time-dependent gradient of the logarithm of the noisy data density - or score function - using a continuous mixture of score matching losses. In this note, we show that such an objective is equivalent to maximum likelihood for certain choices of mixture weighting. This connection provides a principled way to weight the objective function, and justifies its use for comparing different score-based generative models. Taken together with previous work, our result reveals that both maximum likelihood training and test-time log-likelihood evaluation can be achieved through parameterization of the score function alone, without the need to explicitly parameterize a density function.

翻译：最近出现了基于分数的基因化模型,作为传统可能性或隐含方法的一种有希望的替代方法。在基于分数的模型中学习首先需要用连续时间的随机过程来干扰数据,然后用连续的分数匹配损失的组合来匹配噪音数据密度(或分数函数)的根据时间的梯度。在本说明中,我们表明,这样一个目标相当于某些混合加权选择的最大可能性。这一连接提供了一种衡量目标功能的原则性方法,并证明使用它来比较不同的基于分数的基因化模型是有道理的。与以前的工作一起,我们的结果表明,通过将分数函数参数化,可以实现最大的可能性培训和测试时间记录相似性评价,而无需明确参数化密度功能。