Ali, of no fixed address, is currently charged with three counts of murder and was due to face trial next month at Bristol Crown Court.
Anna Vigars KC, prosecuting, told the court earlier that two psychiatrists had prepared reports which had made the reduced pleas available.
“As the court will be aware we have received two psychiatric reports,” she said.
“Both of them, perhaps unsurprisingly in the circumstances of this case, indicating that the partial defence of manslaughter by reason of diminished responsibility is available to Ms Ali.
“The third count, as far as infanticide is concerned, that’s simply because of the youngest child’s age at the time of his death.
“The defence of diminished responsibility applies to all three deaths.
“Having been able to spend some time with the children’s father, Mr Alfil Bash, and to explain the position to him, I am in the position to indicate to the court that were those pleas to be forthcoming they are pleas that would be accepted by the Crown.”