Although almost any sort of fabric glue will work to adhere diamond studs to material, using one that it is made specifically for embellishment is preferable. When considering different glues, think about how often you will wash the item, what kinds of jewels you are using and the type of fabric. Note that while most glues claim to be safe to wash, there is a great deal of variance in their durability. It may be worth it to run some tests to see which would best fit your needs.
Aleene's Jewel-It is an extremely durable fabric glue that is designed specifically for attaching heavier decorations, such as beads or jewels. This glue dries completely clear and will remain bonded even after numerous washings.
Crafty Chica Extreme Embellishment Glue
Crafty Chica Extreme Embellishment Glue is meant to be used to attach all sorts of embellishments to fabric, including glitter, sequins and ribbons. It can also be used for gluing down diamond studs, particularly if they are on the lighter side. It dries clear and is safe to wash.
Fabri-Tac is a very versatile glue that can be used on a wide range of fabrics, including lace. It dries clear and will remain bonded through washings. It is appropriate to use when gluing beads, pearls and diamond studs. However, the reliability of the bond is lowered if the back of the diamonds are coated with silver.
Beacon Gem-Tac Permanent Glue Embellish
This glue can be used to bond diamond studs to a variety of fabrics and even some plastics. It can be washed without damage to the bonding, although it does not claim to have long-term durability. It dries clear.