What happens if a silicon diode measures high value of resistance with the meter leads in both positions?

If the meter is developing more than the necessary forward breakdown voltage of the diode, typically 0.7 volts, then the diode is bad. However, some meters do not generate enough voltage in resistance mode to bias the diode on, unless you flip a switch that enables diode test mode. Use another meter at the same time to measure the voltage across the diode and compare that with the diode's published forward breakdown voltage.