They also spoke of their deep regret over their last conversation with her, revealing how they had been desperate to get off the phone and get back to playing.
Before filming started Prince William and his brother had, however, expressed doubts that they would be able to remember very much of value.
Mr Kent told the latest edition of Vanity Fair: "They prefaced their interviews by saying, 'We don't actually have that many memories of our mum.'"
He added: "One of the [side effects] of grief and bereavement is that memories kind of get suppressed or obliterated, so I don't think they knew, and we certainly didn't know until we began the interview that they would be so candid. But quite quickly when we began the interview, you could almost begin to see the memories surface."
Mr Kent and Ms Gething said that the key to unlocking William and Harry's memories of their mother appeared to be the family photo albums they had kept stored since her death in Paris in 1997.
The filmmakers said it had been the idea of the Duke of Cambridge and his brother to finally "revisit" the albums during filming at Kensington Palace.
"What was great was that a lot of those memories ended up being incredibly joyous," said Mr Kent. "They talked about love, they talked about hugs . . . it felt like the first iteration of [them discovering] a really deep set of memories."
In April - when filming on Diana, Our Mother: Her Life and Legacy had been completed - William and Harry admitted publicly for the first time that they failed to talk to each other enough about the death of their mother and that not doing so had only made matters worse.
The Duke and Prince Harry acknowledged in a video with the Duchess of Cambridge, released as part of their campaign to tackle mental health in Britain, that they had bottled up their feelings about Diana's death in 1997 rather than sharing them.
Ms Gething and Mr Kent revealed that the two princes did not make any subject off-limits, and let them have have complete creative control over the production.
"Obviously they talked very carefully about whether they should make this film," said Ms Gething. "Having decided to make it, they did want it to be a personal film. There were no parameters, rules, or regulations set at all about what should be put in the film or what should be left out of the film.
"It was an amazingly free process and they were very courageous in opening up so much and so publicly, especially given the complex circumstances of their mother's death and the media's involvement in it."
A Channel 4 spokeswoman said they had informed Kensington Palace they plan to air excerpts from the recordings "in a contextualised historical framework at a time when the nation will be reflecting on her life and death".
