Distylium rarely has insect or disease problems. The leaves look like they could have heat stress. Those affected leaves can be removed or they will eventually drop off. It does not look like any fungal infection or insect problem. I am including a paper from Colorado State Extension that may give more information. chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://extension.colostate.edu/docs/pubs/garden/02911.pdf..Brown spots can also come from under or over-fertilization or too much or too little water.  I would remove the affected leaves, but not compost them and watch the plant for more symptoms. If they occur, let us know and we will take another look.

Wanda

Master Gardener volunteer