This is the test circuit with a diode across the inductor:
This is the resulting oscilloscope trace:
Note there are no high voltages or electrical noise, just the exponential decay of the current to zero. Also note that the voltage at the voltage test point (yellow) dips below 0V because of the forward voltage drop of the diode.
A note on terminology
When I first created this tutorial I had the word 'flyback' in mind as the correct term for the diode. After I created it I started to wonder if I had used the wrong term, so I did some research. One person on this forum, who I have a great deal of respect for, said 'flyback' was OK. Some searching on the internet revealed that 'flyback' is used elsewhere to mean the diode across an inductor. However, there are other terms used such as 'kickback diode' and 'free-wheeling diode'. It has since been pointed out to me that 'flyback' also refers to the electron beam in a cathode ray tube returning to its start point to scan a new line.