[D] Why is log likelihood important for Diffusion models?

I was reading [Denoising Diffusion Probabilistic Models](https://arxiv.org/abs/2006.11239) and [Improved Denoising Diffusion Probabilistic Models](https://arxiv.org/abs/2102.09672).

The paper one indicates that they achieve reasonable quality of generated imaged, but in the case of achieved log likelihood fall behind the models which optimize log-likelihood directly.

On the other hand paper two generates even better images, and indicates that they manage to improve the log-likelihood.

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I thought that only FID matters when it comes to image generation?

What does log likelihood indicate in the …

deeplearning diffusion diffusion models likelihood