score_sde VS score_sde_pytorch

Perhaps the ODE interpretation would be helpful (see here and here) which turns DDPMs into neural ODEs using the Fokker-Planck equation so after the initial starting noise, the sampling process is deterministic. If samples are noisy even with the full number of steps then you might need to increase the number of steps further.

Turns out that diffusion models also define a certain differential equation, making it a neural ODE. Then you can just integrate the ODE in the other direction to get the exact inverse for the DDPM (it's not entirely exact b/c of numerical error in the solver, but close enough)

This new approach to generative modelling looks very intriguing.

In a similar ilk, there's this ICLR paper from this year using stochastic differential equations for generative modelling: https://arxiv.org/abs/2011.13456

there's an implementation of score-based models from the paper that showed how score based models and diffusion models are the same here: https://github.com/yang-song/score_sde_pytorch

Someone has already mentioned Neural Ordinary Differential Equations, which is also the first thing that came to mind. There are also extensions to it, where one can use PDEs(Neural Hamiltonian Flows) or even stochastic DEs(Score-Based Generative Models) in the model. All of them covering different but overlapping use cases.

I was considering an unconditional latent diffusion model, but for conditional models, the computation becomes much more complex (we might have to use bayes here). If we use Score-Based Generative Modeling (https://arxiv.org/abs/2011.13456), we could try to find and count all the unique local minima and saddle points, but it is not clear how we can do this...

You can find an implementation here: https://github.com/yang-song/score_sde_pytorch/blob/main/models/ddpm.py