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

imo their implementation is more or less the same as a diffusion model, except score based models would use a numerical ODE/SDE solver to generate samples instead of using the DDPM based sampling method. it might also train on continuous time, so rather than choosing t ~ randint(0, 1000) it would be t ~ rand_uniform(0, 1.)

So do you think it makes a difference in practice, I.e. sampling speed and quality, convergence etc

the speed and quality of score based/diffusion depends on what sampler you use. If youre using euler's method to solve the ODE for example, that might be slower than some of the newer methods developed for diffusion models, like tero karass' ODE solvers. AFAIK there isnt consensus on what the best sampler to use is though.

i dont think it affects training convergence much though since its more or less the same objective.

What's used more in practice?

Diffusion I guess

Diffusion models are effectively score-based, there's a connection with the reversal of the forward process being Gaussian and the noise estimate, effectively you're using scores of Gaussians in the reverse process. The time variable is irrelevant in sense of scale, the discrete time and continuous time essentially do roughly the same, the difference is that one is tied to a specific discretization of the SDE and the other can be solved to arbitrary precision, it's also a difference if you take steps wrt to variance or wrt time. Essentially the continuous formulation should be the limit of the discrete one. So effectively you can take a discrete sampling method and make it a continuous SDE/ODE