Softness and solid angle
In order to get the softest light, you need to have the largest solid angle (like angle but in 3D space) between the subject and the light source.
You can increase your solid angle or softness by 1) increasing the light source size : C0 to C1 or 2) having the source light closer : C0 to C2. I made C1 and C2 having same solid angle: softness will be the same, only the strategy differs.
Role of diffusion
Diffusion in the light source is part of the softening process. The optimal diffusion makes the apparent size (solid angle) of the source as big as the diffuser. A sub optimal diffusion makes the light source smaller, as if it was a combination of strong small light source (light bulb) + big weak light source (diffuser).
You can check the quality of the diffusion by making photography of your flash setup (in manual), and see how uniform is the light coming from the diffuser.
Comments for advanced photography
I shoot with Profoto RFI octa, and I have 2 diffusers stacked inside each octa. It helps indeed having a better (more uniform) light source. Without any diffuser, only the silver umbrella remains, and the apparent size of the light source is barely changed from bare bulb (in the case of Profoto Octa).
With tunable parabolic-like shaped light sources such as Briese Focus, we tune the apparent size of the light source; there is no diffusion but the apparent size is big: that's the secret in order to have soft shadows transitions and crispy textures, which is wanted in beauty commercials.
The actual job of a good photographer is to craft the light; a light source too big makes the subject look flat, a light source too small makes the subject look hard and knife cut.
To improve your skills, I suggest to look at (or photography) the light sources from the subject point of view and try to get a feeling of the coming result.
A practical tactic is to multiply your light sources, instead of having one big light shaper; it's modular and more useful in complex scenes, but for beauty commercials it's not interesting.
For equal solid angle, a bigger (and hence more distant) light source is affecting less the lightning of the subject when it is in movement or extended in space.
Crafting the outdoor light and solid angles
You can without any flash craft the light source size outdoor, with the clouds in the sky: clouds are like new sources and diffusers. A sky without any cloud is almost like bare light bulb; cumulus (especially after storm) in front of blue sky are making an amazing light source; a fully cloudy sky makes the light source as big as possible, contrast and feeling of 3D is minimized.
Adding diffusion makes the light softer by increasing the solid angle when the diffusion is suboptimal; but textures are softened. Increasing the light source size makes shadows transitions softer, but textures are only a bit changed. Working on both is the actual light crafting, and is required to achieve a certain result.