[Defined by Peter Beales in Classic Roses (revised 1997), p. 153:] another bud growing through the centre of the flower

[From Roses: An Illustrated Encyclopaedia & Grower's Handbook, by Peter Beales, p. 440:] Some of the more double-flowered old-fashioned roses will occasionally sprout a malformed bud from their centre... [no one knows for sure why it happens and some roses are more prone to it than others, 'Mme. Isaac Pereire' is an example.]

Note: Zach's photos of 'Toulouse-Lautrec' are good examples of proliferation.

[From Botanica's Roses, p. 488:] 'Prolifera de Redoute' would be a most agreeable shrub were it not for its propensity for proliferation...