Cane-stemmed begonias often develop long "canes" with leaves only on the ends over time, if you already think this one is too open maybe it is not a good plant for you - you would have to keep molesting it with frequent cutting back in order to maintain a more solid appearance than it has right now.

Pinch the terminal buds to encourage new growth along the stem. You can also cut it to the ground (keep the tops to start a new pot). It will take a few weeks for new canes to come on but they should bounce back this summer.

Read up more on Brad's Begonia World about pruning canes. It is quite informative.