Acne, or as it is technically called Acne Vulgaris, has historically been linked to dairy (being the most commonly reported dietary association with acne).
Acne can be furthered and made worse by excessive insulin secretion and appears to also be exacerbated by IGF-1 and Glucose-dependent insulinotropic polypeptide (GIP). In the case of IGF-1, there are repeated correlations between those with acne and higher serum IGF-1 concentrations.
These systemic factors appear to be induced following dairy consumption with insulin, IGF-1, and GIP (which acts to further induce insulin) being increased to levels greater than that of an equicaloric portion of meat (as a comparative protein source).
When looking at serum anabolic factors, dairy protein appears to induce some of these factors to a greater degree than other protein sources
Insulin and IGF-1 both act upon the insulin receptor, the typical signalling pathway includes signalling via PI3K to mTOR/Akt which then induces nuclear ejection of FOX01.
This nuclear ejection of FOX01 tends to be seen as anabolic, as the presence of FOX01 in the nucleus per se is anti-anabolic and ejection hinders its actions. By facilitating anabolic signalling FOX01 ejection can augment androgen-dependent or insulin-receptor (mTOR dependent) anabolism, both the androgen pathway and the mTOR/Akt pathway (downstream of the insulin receptor) increase sebaceous lipogenesis (production of lipids in sebocytes, these cells being skin cells that have a high likelihood of acne production) and activation of the mTOR/Akt pathway can augment androgen signalling.
Anything that activates mTOR/Akt can plausibly increase the efficacy of androgen signalling. Activation of the insulin receptor reliably activates mTOR/Akt (and IGF-1 also acts on this receptor) and is thought to be the main player as there are correlations between diet, insulin and IGF-1 (known to reflect the diet), and acne in humans
A few studies have claimed that reducing total insulinogenic secretions of the diet (limiting grains and dairy) would be beneficial in acne control or at least that the link between dairy and acne requires more investigation.
When looking at surveys, there does appear to be an increased risk of acne associated with dairy products although the relative risk ratios (ranging from 1.12-1.44 depending on dairy product or 1.10-1.19) appears to be weak.
There is a plausible link between dairy consumption and acne but correlational research does not fully support this link; studies tend to be conducted in adolescents (rather than adults) and the results are not too in favor of a strong link; perhaps weak at best
There appears to be a more reliable link between IGF-1 per se than dairy products per se, and although the latter may spike the former current (limited) research does not support a strong relation between dairy and acne