In spite of a number of similarities -- dungeon crawling, large beasties, swords-and-sandals combat -- it would seem the Panta Rhei demo that Capcom demonstrated at Sony's Playstation reveal back in February, for a game then titled Deep Down, has nothing to do do with Dragon's Dogma as previously suspected.
Responding to questions on the Capcom Unity forums over the releases of Dead Rising 3 and Deep Down, Capcom's Christian Svensson rubbished rumours of any connection:
"No new DD product has been announced so there's nothing I can comment on there," he said, with careful phrasing. "For reference DR3 and Deep Down have nothing to do with Dragon's Dogma."
For the record, we'd love to have a new Dragon's Dogma product. If the above remains true, it'll be interesting to see exactly what form Deep Down takes and how Capcom hope to differentiate the title from similar titles in its back catalogue.
Remember, too, that the title "Deep Down" is a working title only at this point.