Oscillators have to build up their output from noise, using regeneration. That regeneration basically bends the noise floor up to become the output spectrum of the oscillator, which causes the noise to rise steeply at low frequency offsets. This was first pointed out by Leeson in about 1966.
G. Sauvage, "Phase Noise in Oscillators: A Mathematical Analysis of Leeson's model", \emph{IEEE Trans. Instrum. Meas.} {\bf IM-26}, 4, pp 408-410 (1977)
D. B. Leeson, "Simple model of feedback oscillator noise spectrum", {\emph Proc. IEEE} February 1966, p. 329
No regeneration, no big noise amplification.
Cheers
Phil Hobbs