Flight crew of a CRJ diverted to a nearby airport when the autoflight speed function failed.

Narrative

During climb passing FL350 for FL380 speed mode was selected and the plane was on autopilot climbing at .74 Mach. ATC gave us a new waypoint to go direct to and a frequency change so our attention was diverted for a very short moment. When I looked up the first thing I noticed was the speed bucket was gone and at the bottom left it showed .59 in the FMA. The airplane had pitched up to try to maintain .59 Mach; the actual airspeed indicator was at about 220KTS. Which wasn't that slow yet and simultaneously with the high VSI rate the altitude captured. This whole process took a very short amount of time and since we were close to our selected altitude the plane started the process of leveling off. After we leveled off everything was normal again. I advised Dispatch and Maintenance. They acknowledged that and we continued on. About 60 miles north of a maintenance facility we got an ACARS message to divert for maintenance; so they could work on the plane. We diverted and landed with no problems all the while continuing to use the autopilot; we landed safely with no problems. Maintenance advised the speed mode function on the autopilot malfunctioned.