What does log_prob do?

As your own answer mentions, log_prob returns the logarithm of the density or probability. Here I will address the remaining points in your question:

• How is that different from log? Distributions do not have a method log. If they did, the closest possible interpretation would indeed be something like log_prob but it would not be a very precise name since if begs the question “log of what“? A distribution has multiple numeric properties (for example its mean, variance, etc) and the probability or density is just one of them, so the name would be ambiguous.

The same does not apply to the Tensor.log() method (which may be what you had in mind) because Tensor is itself a mathematical quantity we can take the log of.

• Why take the log of a probability only to exponentiate it later? You may not need to exponentiate it later. For example, if you have the logs of probabilities p and q, then you can directly compute log(p * q) as log(p) + log(q), avoiding intermediate exponentiations. This is more numerically stable (avoiding underflow) because probabilities may become very close to zero while their logs do not. Addition is also more efficient than multiplication in general, and its derivative is simpler. There is a good article about those topics at https://en.wikipedia.org/wiki/Log_probability.