'On the basis of' doesn't quite work here. 'On the basis of' is used specifically to reference the reason FOR MAKING AN ARGUMENT.
'He was found guilty (the argument) on the basis of huge evidence(the reason).'
'I am writing this essay (the argument) on the basis of recent political events(the reason).'
The reason why it doesn't work in your sentence, is because I think you are saying that sugar is the reason for all diseases. All diseases is not an argument or conclusion. Therefore it doesn't quite work.
Here are some other alternatives:
'All diseases are caused by sugar'
'Sugar is the root cause of all diseases.' (probably the best one)
'All diseases are due to sugar.'