Curious about the differences between latent sampling methods in training

[morphinapg]

I was able to find where this was included here which says:

New latent sampling method
From the original repository code of ldm and textual inversion, when encoding the training data image, a random sample is created for every loop of training. For all this time however, we have been using just one sample from the VAE. This is not how VAE are supposed to work, because its a variational autoencoder, so it encodes data to a normal-distributed latent space, not just one fixed result.
But while tinkering with the code, I discovered that sampling from the mean of latent space can bring better results than one random sample or multiple random samples. So I would like to add options to try out different latent space sampling methods.

'once': The method we have been using for all this time.
'deterministic': My method.
'random': The original method implemented by the original authors. Warning: may increase VRAM usage.

I'm still fairly new at this, so I'm curious about this. To me, it sounds like random would be the method that most closely matches how the generation works? So why would deterministic work better for training, and what exactly does "the mean of latent space" actually mean?

Perhaps it would be useful to explain more in depth of what latent sampling actually is. I have some fairly basic understanding of the way the model and VAE works, but if this specific thing could be explained in more depth that would help me understand exactly what's going on here in relation to the training.

I see a lot of people recommending deterministic and I'm just curious as to why that would produce better results, when random seems like it would make more sense. Also, why is "once" the default, and what does Dreambooth use?