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Latent diffusion models operate in katent space. This space is generated by an encoder and decoded back into pixel space by a decoder. The encoder-decoder form a generator which is trained to have good visual quality through the use of an adversarial loss.
So the encoder produces a latent space that is more efficient to train a diffusion model on, since diffusion models use Unet-like architecture that must be run many times for a single inference. The latent space is restricted by a KL penalty to a Gaussian shape such that any sample from that shape will map through the decoder to a high-quality image. This makes the generative job of the diffusion model much easier because it can focus on content and semantics rather than pixel-level details
You can see the two optimisers at work in the AutoencoderKL class in the Stable Diffusion source code here: https://github.com/CompVis/stable-diffusion/blob/main/ldm/mo...
