"Of course, I did not molest Dylan," the director, 78, writes in an op-ed piece that will appear in Sunday's New York Times." "I loved her and hope one day she will grasp how she has been cheated out of having a loving father and exploited by a mother more interested in her own festering anger than her daughter's well-being."
In the detailed response to Dylan's claims of abuse when she was 7 years old, Allen says the allegations originated from Farrow, now 68, during their "terribly acrimonious breakup" 21 years ago when he began a relationship with her adopted daughter Soon-Yi Previn.
"The self-serving transparency of her malevolence seemed so obvious I didn't even hire a lawyer to defend myself," he writes. I naÏvely thought the accusation would be dismissed out of hand because of course, I hadn't molested Dylan and any rational person would see the ploy for what it was."
Instead, his "raging adversary"'s accusations led to a police case, a lie detector test that he says he passed (but which Farrow didn't take) and a "meticulous investigation" by the Child Sexual Abuse Clinic of the Yale-New Haven Hospital that he says cleared him.
"The district attorney was champing at the bit to prosecute a celebrity case, and Justice Elliott Wilk, the custody judge, wrote a very irresponsible opinion saying when it came to the molestation, 'We will probably never know what occurred,'" says Allen.
The judge, Allen says, was "quite rough on me" out of disapproval of Allen's relationship with Soon-Yi, who was in her 20s at the time when Allen was in his 50s. (Allen and Soon-Yi have now been married for 16 years.)
"He thought of me as an older man exploiting a much younger woman, which outraged Mia as improper despite the fact she had dated a much older Frank Sinatra when she was 19," writes Allen.
After the case, Farrow took custody of Dylan and their children "and we went our separate ways." He never had a relationship with Dylan, now 28.
"Soon-Yi and I made countless attempts to see Dylan but Mia blocked them all, spitefully knowing how much we both loved her but totally indifferent to the pain and damage she was causing the little girl merely to appease her own vindictiveness," writes Allen.
Allen then fuels speculation about the paternity of their son Ronan, now 26, who also has spoken out against him. "Is he my son or, as Mia suggests, Frank Sinatra's?" asks Allen. "Granted, he looks a lot like Frank with the blue eyes and facial features, but if so what does this say?"
He adds: "Even if he is not Frank's, the possibility she raises that he could be, indicates she was secretly intimate with him during our years. Not to mention all the money I paid for child support. Was I supporting Frank's son? Again, I want to call attention to the integrity and honesty of a person who conducts her life like that."
Now, Allen notes, the allegations have returned: "Not that I doubt Dylan hasn't come to believe she’s been molested, but if from the age of 7 a vulnerable child is taught by a strong mother to hate her father because he is a monster who abused her, is it so inconceivable that after many years of this indoctrination the image of me Mia wanted to establish had taken root?"
To bolster his side, Allen quotes Moses, who has supported him, as saying that "my mother often used us as pawns, I cannot trust anything that is said or written from anyone in the family.”
Allen concludes by writing, "No one wants to discourage abuse victims from speaking out, but one must bear in mind that sometimes there are people who are falsely accused and that is also a terribly destructive thing."
He adds as a postscript: "This piece will be my final word on this entire matter and no one will be responding on my behalf to any further comments on it by any party. Enough people have been hurt."
For much more on this story, including exclusive interviews with Dylan Farrow and her brother Moses, who supports Allen, look for this week's issue of PEOPLE and more coverage on PEOPLE.com this week.