On Maximum Likelihood Training of Score-Based Generative Models

• URL: http://arxiv.org/abs/2101.09258v1
• Date: Fri, 22 Jan 2021 18:22:29 GMT
• Title: On Maximum Likelihood Training of Score-Based Generative Models
• Authors: Conor Durkan and Yang Song
• Abstract summary: We show that an objective is equivalent to maximum likelihood for certain choices of mixture weighting. We show that both maximum likelihood training and test-time log-likelihood evaluation can be achieved through parameterization of the score function alone.
• Score: 17.05208572228308
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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