Pn junction under forward bias
the big different between battery and diode is:

Battery is Generator but diode is kind of Electrical load . 

some device exist which name is voltmeter you can check component voltage with it if you connect two head of connector of voltmeter to battery you will see voltage on it . if you connect the voltmeter to diode you cant see any thing and the value of voltmeter display is 0 (zero).

diode have voltage break about 0.7v for silicon diode and 0.3v for germanium diode this is call Gamma voltage .
Nature Gamma voltage is not generator type . it's just waist circuit voltage like under picture .
diode can have voltage but it need battery first.