The 31-year-old also boasted that he would have gone further with the assault and “done as he wanted” had he not feared being caught.
He had been due to face sentence yesterday, but Sheriff Olga Pasportnikov asked for further psychological reports to be carried out.
Fiscal Alison Wylie said he had been in a long distance relationship with Scott Ayres when the offences took place.
When his partner’s home in the south of England was raided by police in the summer, Simpson’s video recording was discovered.
Ms Wylie said: “They previously lived together in Bedford, Northampton, and it was when police visited another male at that address that this came to light. The accused was back in Scotland at the time when this other male was arrested.”
The court heard that police seized all the electronic devices in the property, including a Samsung tablet which belonged to Simspon’s then-partner.
Ms Wylie said that when police reviewed the device they found a “Category” A indecent video showing Simpson lewdly kissing his tiny victim.
The prosecutor added: “The baby was distressed and crying during the video footage.”
Officers later discovered messages Simpson sent Ayres at the time the clip was recorded.
In one message Simpson asked Ayres for his e-mail address to send on the video, and a subsequent one asked whether his former partner had seen it.
The court heard it read: “I didn’t have much time, or I would have done as I wanted.”
The police inquiry shifted north of the border at that point, and Simpson was quizzed about the film.
Officers seized two mobile phones belonging to him, and on one they found two video clips showing children being sexually abused.
It also appeared he had been sharing them with friends in a WhatsApp chat group.
One was graded Category A, the most serious, and featured an infant aged between six months and a year being abused.
The other phone contained footage of a boy aged between four and six being sexually assaulted, as well as other Category B material.
Ayres was also arrested in August and charged with “aiding and abetting in the sexual touching of a child aged under the age of 13” among a string of other offences.
Simpson earlier admitted charges of taking indecent images of a baby, distributing those images, and of possessing indecent images of children.
He also admitted sexually assaulting a child under the age of 13.
Sheriff Pasportnikov said she was concerned about the degree of risk he posed to the public.
She said she would not sentence him until psychological assessments had offered her an answer.
Simpson is due to return to court on Thursday, February 2.
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