So you are managing your models with MLflow, and want to include them in a git repository?

You can do that in a CI/CD process; it would run the mlflow CLI to copy the model you want (e.g. model:/my_model/production) to a git checkout and then commit it, perhaps.

You can also treat MLflow as the 'source control' at runtime and have the production jobs refer to and access the latest model from MLflow directly.

Maybe I don't understand what you're trying to achieve here and you can clarify.