Diffusion will be my epitaph
Let's start with a definition: The spreading of something more widely
Easy enough. In the case of lighting, diffusion spreads the light to cover a wider area. Light diffusers such as the Stofen that are the same size as the light do just that. They let you use your speed light with a wider angle lens with less vignetting. What they don't do is make the light softer. To make the light softer you have to make it larger in relation to your subject. Yes, spreading the light a bit more might let the light bounce off a nearby wall or low ceiling to help fill in shadows a little bit, but the effect is usually minimal unless you are in a very small room with white walls and ceiling.
To make a light source softer, that is to make the shadow edges more gradual, the light has to be made larger. A diffuser right on the light doesn't do this. This extends to studio flash heads, too. Some heads come with a frosted flash tube cover/dome. Some don't. How much effect on the quality of light does the frosted dome offer? Let's look at some examples. Here are eight images made with a Paul C. Buff Einstein and an Interfit Honey Badger. Both of these lights come with a frosted dome. The images with the blue card are from the Einstein and the ones with the pink card are from the Honey Badger. One set was made with a 7-inch metal dish reflector pointed directly at the mannequin, the other set was made with the flash pointing into a 46-inch Photek Softlighter umbrella without its diffusion panel (I wanted to see if the frosted dome on its own made any difference). Can you tell which (A or B) has the frosted dome and which doesn't?
In each of the above pairs of images A is without the dome and B is with the dome. Here is a slider you can use for closer inspection.
I will let you draw your own conclusion about how much the frosted dome has an effect on the softness of the light. Whether you think it softens the light or not, my preference is for a light that does have the dome for its protection of the flash tube and modeling lamp. It also helps match the look of the modeling lamp to the flash tube. I also expect that the dome will help even the spread of light when the flash has a softbox attached. But that is a test for another day.
A few words about the images here. All were made with a Canon EOS M5 camera with the white balance set to Daylight and the light metered for f/5.6. No adjustments to color were made when converting the raw files to jpg for this post. The Honey Badger showed a more neutral color of the white seamless paper background compared to the cool/blue look of the Einstein (which was set to Color mode and about 1/2 power in the umbrella and lower for the 7-inch).
Thanks, as always, for following along!
In case you somehow missed it, my book, Anatomy of a Studio Portrait, is available for order.