You could get an ideal diode and ideal power supply and try the experiment yourself. Oh, no you can't...nobody seems to be supplying ideal components these days.
This is similar to the old question of what happens when an irresistible force meets an immovable object. The voltage across the diode would be undefined. The ideal diode would conduct an infinite amount of current, so we're in the realm of calculus here, but still with conflicting voltage results. This is the reason ideal components don't exist in reality, where limitations on the physical operation of devices result in some solution that balances all the parameters. Ideal parts are approximations of reality, not something that can be implemented.