Ms Faulds, 39, from Kilmarnock, was last seen in Monkton, South Ayrshire, on Sunday 28 April.
Last month Ross Willox, 39, was charged with Ms Faulds’ murder. He made no plea and was remanded in custody.
A Police Scotland spokeswoman said: “On Wednesday, June 12, human remains were discovered in the Galloway Forest, Dumfries and Galloway.”
She added: “The family of Emma Faulds has been made aware of this discovery and police inquiries are ongoing.”