Some frontier labs are reporting positive "adjusted EBITDA" (earnings before interest, taxes, depreciation, and amortization, with extra adjustments to make the figure positive).

Free cash flow (operating profit less investment), actual cash coming in, is deeply in the red.

EBITDA can be a sensible measure of profitability when there isn't much need for additional investment. That doesn't seem to be the case with these operators. They need to invest aggressively to avoid losing customers to competitors. All of these operators have made multi-year commitments to invest more in infrastructure. In addition, they have guaranteed quite a bit of debt to fund it.

Maybe it all will work out fine (and I sure hope it does!), but I didn't see any hard data from the OP, or from you, supporting that view.

Definitely. The question is: Is it enough to recoup the enormous capital costs and justify the level of investment they've received. I think there's a decent chance that it will be. But maybe not. And the longer they keep focusing on training new models more so than on inference, the more uncertain I become that it's all going to work out.

Who is the "they" that are turning profits?

Labs are playing money games with EBITDA, which is not uncommon, but also hides the extent to which they are in the red (deeply, deeply, in the red, and projected by them to get worse).