[D] Diffusion vs MCMC as sampling algorithms

I was recently reviewing the diffusion methods used in Stable Diffusion and my mind wandered to Markov Chain Monte Carlo, which got me thinking - are there important theoretical similarities / differences between these methods?

A bit of background:

* Intro to Stable Diffusion: A nice illustrated guide by Jay Alammar [https://jalammar.github.io/illustrated-stable-diffusion/](https://jalammar.github.io/illustrated-stable-diffusion/)
* Intro to MCMC: Stanford CS168 notes by Tim Roughgarden and Gregory Valiant [http://timroughgarden.org/s17/l/l14.pdf](http://timroughgarden.org/s17/l/l14.pdf)
* The Metropolis-Hastings (MH) algorithm, a specific MCMC algorithm: [https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings\_algorithm](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm)

My own stream-of-consciousness thoughts: …

algorithms diffusion machinelearning mcmc sampling