Spurred by another discussion elsewhere, Lilium cernuum is one of the favorites in breeding parentage, because if its mix of floral color genes. Besides the high quality pink color, this species possesses at least one color blocking gene that has the ability to turn off the expression of certain color genes. In simplistic terms for example, if a lily has an orange gene, that lily is orange. If that orange lily also has a color blocking gene for that color orange, then the lily would not be orange. Then would it be white? Perhaps. Or, another color that has always been present might show up because the strong orange color is no longer there to overshadow it. (Similar to why fall leaves turn color.... the reds and yellows are there all summer, too, but the green is so predominant that it overshadows the other colors.)
It is not known with surety whether Lilium cernuum album is white because of the lack of other color genes, or because blocking color genes are employed. Most alba forms of other species (not just lilies) are due to the absence of other colors, and the presence of whatever constitutes a "white" gene. Also with most alba forms, the mutation or the combining of genes that results in its expression, may not be that rare, and it is probable that in any species, alba forms can pop up as unrelated specimens in diverse populations.
Back to my statement: "It is not known with surety whether Lilium cernuum album is white because of the lack of other color genes, or because blocking color genes are employed", the hard data of the different forms in the trade would suggest the latter. This then, would explain the diversity of L. cernuum album forms, because of the individually inherent diversity of color genetics. The other explanation would be that color has crept into the lines of L. cernuum album through accidental pollination by normally colored L. cernuum.