The speaker says the diffusion-based stochastic differential equation approach is much cheaper than actual MCMC and avoids accept-reject steps and local minima while transforming an initial density into a final density.

“So and of course if you go down to the latent ed point at time point zero point six, you end up kind of having effectively a different density. So now we have this time dimension as an additional variable. So this is what you pay for. But in general this is much much cheaper still than uh needing to do like the actual M_C_M_C_ process because now you just you follow essentially a density so with like the randomised uh like i you randomly”

“uh inject more i uh noise at every time step. But you no longer need to have like this accept reject step, you no longer have the problem of like local minima and so on, because essentially what you did is you've rephrased this as a stochastic differential equation which um”

“essentially then goes from like the the initial density to final density. And this is just by basically paying for with one additional variable which effectively indexes over the latents.”

“And this gives you a huge improvement because you no longer need to uh do effectively this this time, it still exists in M_C_M_C_ like it's the the the sampling steps. But effectively you amortize that as well and that makes it a lot cheaper.”