Lots of distributions have "origin myths", or examples of physical processes that they describe well:
- You can get normally distributed data from sums of uncorrelated errors via the Central Limit Theorem
- You can get binomially distributed data from independent coin flips, or Poisson-distributed variables from a limit of that process
- You can get exponentially distributed data from waiting times under a constant decay rate.
And so on.
But what about the Laplace distribution? It's useful for L1 regularization and LAD regression, but it's hard for me to think of a situation where one should actually expect to see it in nature. Diffusion would be Gaussian, and all the examples I can think of with exponential distributions (e.g. waiting times) involve non-negative values.