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.

本文提出基于分数的扩散模型的最大似然训练方法，其中采用一种特定的权重方案，目标函数上界拘束负对数似然函数，达到了与当前最先进的自回归模型同等水平的负对数似然性能，验证了该方法在多个数据集、随机过程和模型结构上的有效性。