According to the Huygens–Fresnel
principle, every point of the wavefront is a new spherical wave source. Of course, you don't see infinite individual waves; what you see is the result of summing (interference) infinite waves.
This means there is always interference, even if there are no obstacles. Diffraction would be a consequence of blocking part of the wavefront, so the waves which are left interfere in some fancy way. This principle can be used to describe refection, refraction and diffraction.
For a single slit several times bigger than the wavelength (the dots are the wave sources):
If the slit is as big as the wavelength you see a single spherical wave (I wouldn't be sure to consider this diffraction at all):
There is something similar to the Huygens–Fresnel principle in quantum electrodynamics. The path integral formulation says that when light (and any other particle) travels to a point $A$ to a point $B$, you have to sum every possible trajectory. Each trajectory has the same probability, they only differ in phase.
So for the two slit, if you compute each possible path you would get the classical result.
So I would say that diffraction is a particular case of interference where some part of the wavefront has been blocked.
But the difference between interference and diffraction is not clear. As Feynman said: "no-one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them".