For babies, no. For adults who need diapers as a result of a medical condition, yes. You cannot include in medical expenses the amount you pay for diapers or diaper services, unless they are needed to relieve the effects of a particular disease (2013 Pub. 502, p. 15).
This wording stems from Rev. Rul. 55-261. Specifically, that ruling states: "16. Maternity clothing, antiseptic diaper service, wigs, toothpaste.—Amounts expended for the preservation of general health or for the alleviation of physical or mental discomfort which is unrelated to some particular disease or defect are not expenses for medical care as defined in section 23(x) of the Code. Expenditures for maternity clothing, antiseptic diaper service, wigs, and toothpaste, are held to be personal expenses, the deduction of which is prohibited by section 24(a)(1) of the Code. O. G. Russell v. Commissioner, Tax Court Memorandum Opinion, entered November 6, 1953."

In PLR 8137085, disposable diapers were deductible for taxpayer's 4-year old daughter who had Aicardi syndrome, which left her incontinent as a result. The child was well past the age when diapers would be a normal living expenses, but the expenses were held to be deductible medical expenses. The courts have not ruled specifically on a dementia, Parkinson's or an Alzheimer's patient, seemingly because the IRS hasn't challenged the deduction. Presumably, they are simply denying a deduction for diapers of your typical infant.