It's not finite but inflation is paid out to ETH holders in proportion to the amount of ETH they stake for validation, so on the balance, ETH holdings experience no dilution. Rather, there is constant (and gradual, at a rate of about 1-2% per year) transference of ETH value from inactive holders, who don't stake their ETH, to active holders, who do.

So I think ETH can be both digital oil (or digital solar, if you want to be PC) and digital gold.