I have that kind of damage when I forget a plant I've stuck someplace to water it, and the sun comes around the corner and cooks it, especially if the leaves are wet. Doesn't look like any disease I've seen--tho' I'm sure there are plenty! I'd just take off the damaged leaves. An early begonia 'guru' of mine said plants can never repair a damaged leaf, but will expend energy trying to, so take 'em off. I'm not sure they actually do try to repair 'em, but I do know they can't, and the plant will do better without them. Often the little bud at the leaf base will start growing and you'll have a bushier plant.

Greenelbows is right. That looks like sunburn to me. Plant probably needs shadier conditions and little drink of water with a pinch of epsom salts in it.

Lainey

While on the subject of leaf "disease," what is the best way to deal with mildew forming on the leaves of tuberous begonias? Spray???

Move it to a shadier spot for a while and water well. Pinch off the damaged leaves and maybe even most of the leggy stems. When it recovers you can move it back to a sunnier locale. This is Dragon Wings and it can take full sun as long as it doesn't dry out.