Add diffusion model as inference network

[vpratz]

As we have multiple people working on this, I want to use this issue to coordinate a bit.

@arrjon @niels-leif-bracher What is the state of your projects/implementations, and what are your plans regarding the integration of diffusion models as inference networks into BayesFlow?

I have an implementation of the EDM/k-diffusion from [1], similar in style to the FlowMatching class.
I assume that our implementations are probably quite similar, and I think it would be nice to get one into the experimental module, so we can test it out and compare it to flow matching.

@stefanradev93 I think you are the one with the best overview, so if you have thoughts, please also share them here :)

[1] Elucidating the Design Space of Diffusion-Based Generative Models: https://arxiv.org/abs/2206.00364

[stefanradev93]

@arrjon @niels-leif-bracher have implementations of various score-based models according to the classification x/epsilon/u prediction (https://diffusionflow.github.io/), also similar to FlowMatching.

I believe we can sync the implementations quite well. You can PR your code when ready and add @arrjon / @niels-leif-bracher as reviewers to start the discussion going.

[arrjon]

I have a quite general implementation using also code from @niels-leif-bracher, which follows the ideas in this nice overview paper Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation by Kingma et. al.: So different noise schedules, different parameterizations and discrete and continuous (SDE) formulations. My code is not yet transformed to be backend agnostic, but I have it on my to do list. This should then be easily mergable with your EDM implementation.

[arrjon]

So the best solution might be to start with your code @vpratz and I add my stuff from there as @stefanradev93 suggested?

[vpratz]

Thanks for your comments, this sounds good to me :)

[vpratz]

Closed by #408