A method of forming a polycrystalline diamond cutting element includes assembling a diamond material, a substrate, and a source of catalyst material or infiltrant material distinct from the substrate, the source of catalyst material or infiltrant material being adjacent to the diamond material to form an assembly. The substrate includes an attachment material including a refractory metal. The assembly is subjected to a first high-pressure/high temperature condition to cause the catalyst material or infiltrant material to melt and infiltrate into the diamond material and subjected to a second high-pressure/high temperature condition to cause the attachment material to melt and infiltrate a portion of the infiltrated diamond material to bond the infiltrated diamond material to the substrate.