Shia LaBeouf and Wife Mia Goth Separated About a Year Ago

Shia LaBeouf is going through it this week following an alleged drunken fight and arrest in New Orleans -- and that's on top of a split from his wife Mia Goth ... a source tells TMZ the couple has been separated for about a year.

And Page Six reports Shia moved to New Orleans after the separation to be closer to family. His time Down South has not been smooth, as he's now dealing with the aftermath of a savage beatdown and subsequent arrest early this morning.

Meanwhile, we got a picture of Mia heading into a private gym in L.A. today. She went incognito for her first public outing since news of their split broke, opting to wear a New York Giants cap and sunglasses on the overcast winter day.

Here's the last time we saw the couple together, out for a walk in L.A. in January last year.

As we reported ... Shia was allegedly causing trouble at a bar in the French Quarter last night and allegedly punched one of the staff members. This started an epic brawl, which ended horribly for Shia. He basically got his ass kicked until the police showed up.

The "Transformers" star was taken to the hospital for his injuries and later arrested and charged with 2 counts of simple battery.

The incident is not a good sign for Shia's sobriety journey ... he entered court-mandated rehab after a 2017 arrest in Savannah, Georgia, for public drunkenness and disorderly conduct. Since then, he's been intermittently sober ... but has sought long-term sobriety support, including therapy and structured recovery programs.