Are any inference providers currently making profit (on inference, I know google makes money)?
Third parties selling open-weight inference on OpenRouter are surely selling on a profit. Zero reason to subsidize it.
Selling inference is not fundamentally different from selling compute - you amortize the lifetime cost of owning and operating the GPUs and then turn that into a per-token price. The risk of loss would be if there is low demand (and thus your facilities run underutilized), but I doubt inference providers are suffering from this.
Where the long-term payoff still seems speculative, is for companies doing training rather than just inference.
All of them. It's simply impossible to sell tokens by usage at a loss now. You'll be arbitraged to death in a few days. It only makes sense to subsidize cost if you're selling a subscription.
Google definitely makes money in other areas. Do they make money on inference?
Pretty much every major American inference provider claims to make a profit on API-based inference. Consumer plans might be subsidized overall, but it's hard to say since they're a black box and some consumers don't fully use their plans