Diffusion models essentially use a stochastic differential equation to produce samples. An MCMC method that produces samples using such equations, often known as Langevin diffusions, are called the Unadjusted/Metropolis-Adjusted Langevin algorithm(s).

Typically we don’t use the metropolis adjustment in practice and so these methods aren’t truly Metropolis-Hastings algorithms, they are just discretized SDEs. The purpose of the adjustment is to reduce bias and ensure convergence to a particular distribution but these are lesser concerns in diffusion models, particularly with small enough step size.

If you have inexpensive features then you could try and build a Determinantal Point Process, a model for sampling diverse subsets (diversity defined via the features and an appropriate kernel). The downside is that this method, at worst, typically scales poorly (O(N^3 )) with the number of samples although there is recent work in this field to speed up inference. I can’t say a priori if it is fast enough for your task.