I don't think SAS has diffusion models as a standard feature of the (econometrics part of the) software.
Diffusion models are used for time series forecasting ... mainly when the time series (before forecasting) is short.
You can estimate "Jump Diffusion" though:
https://support.sas.com/resources/papers/proceedings20/5079-2020.pdf
Not sure why you have asked this question in the "Operations Research / Management Science" - board , and not in the "econometrics / forecasting" - board.
Ciao,
Koen