A lot of the discussion around basic income takes place in the context of Modern Monetary Theory. I mean, it kind of has too, because otherwise basic income is pretty unaffordable. I've done the math, it is possible but really hard.
To significantly oversimplify one stream of thought in Modern Monetary Theory, the idea is that you grow the money supply through government programs and shrink it through taxation and that's how you keep inflation in check. (That's also why you don't have to worry about the cost of government programs. The government can print and spend as much money as it wants, because doing so is just growing the money supply. And if inflation starts to go up, you just raise taxes in response.)
If you look at what's happening with inflation right now, some of it is wage growth pressure. You could argue that some of it was growth in the money supply - although I would give serious side eye to that argument because not very much was given out in those stimulus checks. But if you really look at what's driving price increases, you have to look at what's happening internally to companies. Wages are growing, yes, but prices are growing faster than wages. Why? Because corporate profits are growing even faster.
So one of the primary factors driving inflation isn't the increase in the money supply, or workers wage increases - it's companies taking advantage of the inflation to raise their prices even more. If you look at the numbers, if worker wage increases would require a 5% increase in prices, companies are taking that and then raises their prices 10% and taking the difference as profits. Corporate profits were already at all time highs, so they absolutely do not have to do that. It's effectively price gouging.
So if we look at a basic income, if we implement it in isolation, it's reasonable to believe the same thing will happen. Companies will simply raise their prices so that the top 10% (who own the majority of the stock), walk away with all that new money added to the supply.
If we really want basic income to have the impact we all hope it will have, we have to implement it alongside income and wealth caps. Basically, if you actually want a more equitable (and healthier for everyone) distribution of wealth, then you have to put hard limits on hoarding. And that's how you manage the money supply to manage inflation. You implement basic income alongside 100% wealth and income taxes above a certain level.