The forward voltage Vf of a diode
If this is a small signal silicon diode, then use Vf=0.6V @ 1mA
But reducing the current by a log scale also reduces the forward voltage on a linear scale up to 5 decades down. Above this, the bulk resistance limits the minimum resistance and thus voltage rise with the current before its power limit.
For Power diodes, the internal bulk resistance limits the rise in voltage where they are rated for Vf at Idc(max).
For specific diode VI graphs, one needs a part number or datasheet below and above 1 mA.  There are several non-ideal factors but common curves are available on the web.
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