Well, not exactly infinite, but you can generate a large number of addresses from a single private key. This is done through the use of hierarchical deterministic (HD) wallets.

With HD wallets, you can generate a tree-like structure of public and private keys (addresses) from a single root seed (the initial private key). It's this setup that allows for multiple addresses to be derived from one original key.

But remember mate - while it's technically possible to create many addresses this way, it's always important to keep your private keys secure! In the wrong hands, they could lead someone right to your bitcoins.